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Study sets matching "law of sines sines cosines"

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Study sets matching "law of sines sines cosines"

12 terms
Law of Sines and Law of Cosines
a=7.8... <C=84.8°... <B=44.19
no solution
a=9... <B=58.2°... <C=82.4°
<A=112.2°... <B=28.8°... <C=39°
solve the triangle using the law of cosines if (round ANSWERS…
How many triangles, if any, will result from this set of data…
solve the triangle using the law of cosines if (round ANSWERS…
solve the triangle if (round ANSWERS to the nearest tenth) :…
a=7.8... <C=84.8°... <B=44.19
solve the triangle using the law of cosines if (round ANSWERS…
no solution
How many triangles, if any, will result from this set of data…
6 terms
Law of Sines and Cosines
law of sines formula
area of a triangle
ambiguous case
law of cosines
used to solve SSA triangles
used to solve SAS and SSS
law of sines formula
area of a triangle
20 terms
Law of Sines and Law of Cosines
find the area of ∆DEF, if (round answe…
solve the triangle using the law of co…
How many triangles, if any, will resul…
solve the triangle using the law of co…
63.9 units²
a=7.8... <C=84.8°... <B=44.19
no solution
a=9... <B=58.2°... <C=82.4°
find the area of ∆DEF, if (round answe…
63.9 units²
solve the triangle using the law of co…
a=7.8... <C=84.8°... <B=44.19
11 terms
Law of Sines & Law of Cosines
Law of Sines
Area of Oblique Triangle (angle A)
Area of Oblique Triangle (angle B)
Area of Oblique Triangle (angle C)
1/2(bc)(sin A)
1/2(ac)(sin B)
1/2(ab)(sin C)
Law of Sines
Area of Oblique Triangle (angle A)
1/2(bc)(sin A)
18 terms
Law of Sines and Law of Cosines
63.9 units²
a=7.8... <C=84.8°... <B=44.19
no solution
a=9... <B=58.2°... <C=82.4°
find the area of ∆DEF, if (round answer to the nearest tenth)…
solve the triangle using the law of cosines if (round ANSWERS…
How many triangles, if any, will result from this set of data…
solve the triangle using the law of cosines if (round ANSWERS…
63.9 units²
find the area of ∆DEF, if (round answer to the nearest tenth)…
a=7.8... <C=84.8°... <B=44.19
solve the triangle using the law of cosines if (round ANSWERS…
11 terms
Law of Sines and Law of Cosines
solve the triangle using the law of co…
solve the triangle using the law of co…
solve the triangle if (round ANSWERS t…
find side a if (hint* use law of sines…
a=7.8... <C=84.8°... <B=44.19
a=9... <B=58.2°... <C=82.4°
<A=112.2°... <B=28.8°... <C=39°
a=10
solve the triangle using the law of co…
a=7.8... <C=84.8°... <B=44.19
solve the triangle using the law of co…
a=9... <B=58.2°... <C=82.4°
20 terms
Law of Sines and Law of Cosines
find the area of ∆DEF, if (round answe…
solve the triangle using the law of co…
How many triangles, if any, will resul…
solve the triangle using the law of co…
63.9 units²
a=7.8... <C=84.8°... <B=44.19
no solution
a=9... <B=58.2°... <C=82.4°
find the area of ∆DEF, if (round answe…
63.9 units²
solve the triangle using the law of co…
a=7.8... <C=84.8°... <B=44.19
20 terms
Law of Sines and Law of Cosines
find the area of ∆DEF, if (round answe…
solve the triangle using the law of co…
How many triangles, if any, will resul…
solve the triangle using the law of co…
63.9 units²
a=7.8... <C=84.8°... <B=44.19
no solution
a=9... <B=58.2°... <C=82.4°
find the area of ∆DEF, if (round answe…
63.9 units²
solve the triangle using the law of co…
a=7.8... <C=84.8°... <B=44.19
11 terms
Law of Sines and Law of Cosines
Law of Cosines: case 1
Law of Cosines: case 2
Law of Sines: case 3
Law of Sines: case 4
Use this in a non-right triangle when you know all three side…
Use this in a non-right triangle when you know two sides and…
Use this in a non-right triangle when you know two sides and…
Use this in a non-right triangle when you know two angles and…
Law of Cosines: case 1
Use this in a non-right triangle when you know all three side…
Law of Cosines: case 2
Use this in a non-right triangle when you know two sides and…
13 terms
Law of Sines and Law of Cosines
solve the triangle using the law of co…
solve the triangle using the law of co…
solve the triangle if (round ANSWERS t…
find side a if (hint* use law of sines…
a=7.8... <C=84.8°... <B=44.19
a=9... <B=58.2°... <C=82.4°
<A=112.2°... <B=28.8°... <C=39°
a=10
solve the triangle using the law of co…
a=7.8... <C=84.8°... <B=44.19
solve the triangle using the law of co…
a=9... <B=58.2°... <C=82.4°
9 terms
law of sines/cosines
laws of sines
law of cosines for angle A
law of cosines for angle B
law of cosines for angle C
∠A = cos−1((b^2+c^2−a^2)/(2bc))
∠B = cos−1((a^2+c^2−b^2)/(2ac))
∠C = cos−1((a^2+b^2−c^2)/(2ab))
laws of sines
law of cosines for angle A
∠A = cos−1((b^2+c^2−a^2)/(2bc))
12 terms
Law of sines/cosines
Law of Sines
Angle side angle
Angle side side
Area triangle SAS
sin a/A =sin b/B= sin c/C
Sine triangle, non-ambiguous
Ambiguous case, sine triangle
(1/2) absinC
Law of Sines
sin a/A =sin b/B= sin c/C
Angle side angle
Sine triangle, non-ambiguous
9 terms
Law of Sines, Cosines
what is the law of sines?
what is the law of sines used for?
how do you find the area using the law…
how do you find the perimeter?
sinA/a= sinB/b= sinC/c ... a/sinA = b/sinB = c/sinC
non right angle triangles
.5(side)(side)(sin*included angle) ... area= 1/2absinC... area= 1/…
add up all three sides
what is the law of sines?
sinA/a= sinB/b= sinC/c ... a/sinA = b/sinB = c/sinC
what is the law of sines used for?
non right angle triangles
8 terms
Law of Sines/Law of Cosines
Law of Sines
Find a
Find b
Find c
sinA/a = sinB/b = sinC/c
a^2 = b^2 + c^2 - 2bc(cosA)
b^2 = a^2 + c^2 - 2ac(cosB)
c^2 = b^2 + a^2 - 2ab(cosC)
Law of Sines
sinA/a = sinB/b = sinC/c
Find a
a^2 = b^2 + c^2 - 2bc(cosA)
10 terms
Law of Sines and Law of Cosines
Law of sines (AAS, ASA)
Law of cosines (SSS, SAS) 1
Law of cosines (SSS, SAS) 2
Law of cosines (SSS, SAS) 3
(a/sinA) = (b/sinB) = (c/sinC)
c^2 = a^2 + b^2 - 2abcosC
b^2 = a^2 + c^2 - 2accosB
a^2 = b^2 + c^2 - 2bccosA
Law of sines (AAS, ASA)
(a/sinA) = (b/sinB) = (c/sinC)
Law of cosines (SSS, SAS) 1
c^2 = a^2 + b^2 - 2abcosC
10 terms
Law of Sines and Law of Cosines
you use this law when given a triangle…
you use this law when given a triangle…
Law of Sines: What is the formula to f…
Law of Sines: What is the formula to f…
law of sines
law of cosines
sinA/a = sinB/b = sinC/c
a/sinA = b/sinB = c/sinC
you use this law when given a triangle…
law of sines
you use this law when given a triangle…
law of cosines
16 terms
Law of Sines & Law of Cosines
AAS
ASA
SSA
SSS
Law of Sines
Law of Sines
Law of Sines / ambiguous
Law of Cosines
AAS
Law of Sines
ASA
Law of Sines
16 terms
Law of Sines & Law of Cosines
AAS
ASA
SSA
SSS
Law of Sines
Law of Sines
Law of Sines / ambiguous
Law of Cosines
AAS
Law of Sines
ASA
Law of Sines
Law of Sines & Law of Cosines
a/sinA
SSA... Opposite< height (acute)
SSA... Opposite</= adjacent (obtuse)
SSA... Opposite= height (acute)
b/sinB=c/sinC
No triangle
No triangle
One triangle
a/sinA
b/sinB=c/sinC
SSA... Opposite< height (acute)
No triangle
7 terms
Law of Sines and Law of Cosines
Law of Sines
Law of Cosines
Law of Cosines Rule of Thumb with SAS
Law of Cosines Rule of Thumb with SSS
a/sinA = b/sinB... AAS... ASA... SSA (many options)
SAS... SSS... a^2=b^2+c^2-2bc(cosA)
Find smallest angle next
Find the largest first
Law of Sines
a/sinA = b/sinB... AAS... ASA... SSA (many options)
Law of Cosines
SAS... SSS... a^2=b^2+c^2-2bc(cosA)
9 terms
Law of Sines / Law of Cosines
LoS No Triangle
LoS One Right Triangle
LoS One Triangle
LoS Two Triangles
a<h
a=h
A is obtuse
ASS... a<90°... h<a<b
LoS No Triangle
a<h
LoS One Right Triangle
a=h
10 terms
Law of Sines and Law of Cosines
Obtuse- opposite is > adjacent
Obtuse- opposite is < or = adjacent
Acute- opposite is < height
Acute- opposite is = to height
1 triangle
0 triangles
0 triangle
1 triangle (right)
Obtuse- opposite is > adjacent
1 triangle
Obtuse- opposite is < or = adjacent
0 triangles
8 terms
Law of Sines & Law of Cosines
Law of Sines Formula (both ways)
Area of an Oblique Triangle (SAS)
How to find the height:
Give the conditions for when angle A i…
sinA/a = sinB/b = sinC/c OR a/sinA = b/sinB = c/sinC
A = 1/2bcSinA OR 1/2acSinB OR 1/2abSinC
h = bsinA
a ≤ b - no solution ... a > b - 1 solution
Law of Sines Formula (both ways)
sinA/a = sinB/b = sinC/c OR a/sinA = b/sinB = c/sinC
Area of an Oblique Triangle (SAS)
A = 1/2bcSinA OR 1/2acSinB OR 1/2abSinC
16 terms
Law of Sines/Law of Cosines
law of sines
which congruences use LOS
ASS: obtuse, opp > adj
ASS: obtuse, opp < adj
sin(A)/a = sin(B)/b = sin(C)/c
AAS... ASA... ASS- ambiguous case
1 triangle
0 triangles
law of sines
sin(A)/a = sin(B)/b = sin(C)/c
which congruences use LOS
AAS... ASA... ASS- ambiguous case
9 terms
Law of sines and law of cosines
Law of sines
Law of sines: A,B,C are
Law of sines: a,b,c are
Law of sines
Sin A Sin B Sin C... _______= ______=_______... a .......... b ...…
Angles
Opposite angles of same name
Any time you know the measure of one angle and the length of…
Law of sines
Sin A Sin B Sin C... _______= ______=_______... a .......... b ...…
Law of sines: A,B,C are
Angles
16 terms
Laws of Sines and Cosines
Law of Sines
Area of an Oblique Triangle
Law of Cosines (finding a missing side…
Law of Cosines (finding a missing angle)
a/sinA = b/sinB = c/sinC
A=(1/2)bc(sinA)
a^2 = b^2 +c^2 -2bc(cosA)
cosA = (b^2 + c^2 - a^2)/(2bc)
Law of Sines
a/sinA = b/sinB = c/sinC
Area of an Oblique Triangle
A=(1/2)bc(sinA)
10 terms
Law of sines/cosines
ASA
AAS
ASS
SSS
Law of sines
Law of sines
Law of sines
Law of cosines
ASA
Law of sines
AAS
Law of sines
7 terms
law of sines/cosines quiz
when do u use law of sines
when do u use law of cosines
law of sines
law of cosines
ASA, AAS, SSA
SSS, SAS
sinA/a = SinB/b
a^2=b^2+c^2-2bccosA
when do u use law of sines
ASA, AAS, SSA
when do u use law of cosines
SSS, SAS
8 terms
Law of Sines/Cosines
Law of sins
Law of Cosines
A^2
B^2
SinA/a=SinB/b=SinC/c
...
b^2+c^2-2bcCosA
a^2+c^2-2acCosB
Law of sins
SinA/a=SinB/b=SinC/c
Law of Cosines
...
10 terms
Law of Sines/Cosines
Law of Sines
Ambiguous Case (A is acute)
Ambiguous Case (A is obtuse)
Area law of Sines
ASA... AAS... SSA *Ambiguous case
a<h, no solution... a=h, one triangle (right)... a≥b, one triangle…
a≤b, no solution... a>b, one triangle
1/2(b)(h)... 1/2ac(sin B)... 1/2ab(sin C)... 1/2bc(sin A)
Law of Sines
ASA... AAS... SSA *Ambiguous case
Ambiguous Case (A is acute)
a<h, no solution... a=h, one triangle (right)... a≥b, one triangle…
14 terms
Law of sines/cosines quiz
Law of sines works for what triangles
Law of cosines works for what triangles
Area formula for SAS
Semi perimeter (sss)
AAS SSA
SAS SSS
.5•a•b•sinc
.5(a+b+c)
Law of sines works for what triangles
AAS SSA
Law of cosines works for what triangles
SAS SSS
17 terms
Law of sines and cosines
H
No triangle
One right triangle
Two triangles
H=bSINA
A<h
A=h
H<a<b
H
H=bSINA
No triangle
A<h
14 terms
Law of Sines and Cosines
Law of Sines (option 1)
Law of Sines (option 2)
Ambiguous Triangle
Law of Cosines (A)
sinA/a = sinB/b = sinC/c
a/sinA = b/sinB = c/sinC
when we are given a single angle. (SSA---sin)... 1. No triangle…
a2 = b2 + c2 - 2bccos A
Law of Sines (option 1)
sinA/a = sinB/b = sinC/c
Law of Sines (option 2)
a/sinA = b/sinB = c/sinC
16 terms
Law of sines/cosines
Law of sines formula
Opp angles =
ASA or AAS
SSA
a/sinA = b/sinB = c/sinC
Law of sine
Solve w law of sine
Check for 2 triangles
Law of sines formula
a/sinA = b/sinB = c/sinC
Opp angles =
Law of sine
13 terms
Law of Sines/Cosines
Law of Sines Patterns
Special case in Law of Sines
If opposite angle > adjacent (LOS)
If opposite angle < adjacent (LOS)
ASA... AAS... SSA
SSA
1 solution
3 possible solutions
Law of Sines Patterns
ASA... AAS... SSA
Special case in Law of Sines
SSA
7 terms
Law of Sines VS. Law of Cosines
Law of Cosines
Law of Sines
45
137
What is the measure of BC?
What is the measure of ∠A?
Law of Cosines
Law of Sines
7 terms
Law of Sines and Cosines
Law of Cosines
Law of Sines
Ambiguous Case
a=h (SSA only)
SAS, SSS
ASA, AAA, AAS, SSA
SSA
One solution
Law of Cosines
SAS, SSS
Law of Sines
ASA, AAA, AAS, SSA
9 terms
Law of Cosines and Sines
sin(A) / a
b² + c² - 2bc cos(a)
a² + c² - 2ac cos(b)
a² + b² -2ab cos(c)
sin(B) / b
b² + c² - 2bc cos(a)
a² + c² - 2ac cos(b)
9 terms
Law of Sines and Cosines
Law of Sines
Law of Cosines
For SAS triangles using law of cosines
For SSS triangles using law of cosines
sinA/a=sinB/b=sinC/c
a^2=b^2 + C^2 -2bc(cosA)
find side first, then solve for the smallest angle
Solve for the largest angle first, then next largest
Law of Sines
sinA/a=sinB/b=sinC/c
Law of Cosines
a^2=b^2 + C^2 -2bc(cosA)
11 terms
Law of Sines/Cosines
What is the formula for the law of sin…
What is the formula for the law of cos…
When does the law of sines have partic…
In the case of an ASS triangle, how do…
side a/sinA = side b/sinB
a²=b²+c²-2×b×c×cos(A)
When it's an ASS triangle
If sin(x) > 1
What is the formula for the law of sin…
side a/sinA = side b/sinB
What is the formula for the law of cos…
a²=b²+c²-2×b×c×cos(A)
16 terms
Law of Cosines and Sines
cosA
cosB
cosC
b²+c²-a²/ 2bc
a²+c²-b²/ 2ac
a²+b²-c²/ 2ab
b²+c²-2bccosA
cosA
b²+c²-a²/ 2bc
cosB
a²+c²-b²/ 2ac
14 terms
Law of Sines/Cosines
Law of cosines equation
Law of cosines re-arranged to find ang…
How many sides and angles must be pres…
Law of sines equation
c²=a²+b²-2abcos(C)
cos(C)= a²+b²-c²÷2ab
two
a/sinA=b/sinB=c/sinC
Law of cosines equation
c²=a²+b²-2abcos(C)
Law of cosines re-arranged to find ang…
cos(C)= a²+b²-c²÷2ab
8 terms
Law of Sines and Cosines
ASA
AAS
SSA
Two angle measures and any side length.
Law of Sines
Law of Sines
Law of Sines
Law of Sines
ASA
Law of Sines
AAS
Law of Sines
14 terms
law of sines/cosines formulas
1/2absinC= 1/2bcsinA = 1/2acsinB
a/sinA = b/sinB = c/sinC
AAS, ASA, SSA
ASS
area of oblique triangles (law of sines)
law of sines
law of sines is used with what types of triangles: ____ _____…
ambiguous case:
1/2absinC= 1/2bcsinA = 1/2acsinB
area of oblique triangles (law of sines)
a/sinA = b/sinB = c/sinC
law of sines
7 terms
Law of Sines and Cosines
Straight forward cases of Law of Sines?
The ambiguous case of Law of Sines is…
We can't solve oblique triangles that…
We use Law of cosines when we have:
ASA, AAS
ASS
AAA
SAS, SSS
Straight forward cases of Law of Sines?
ASA, AAS
The ambiguous case of Law of Sines is…
ASS
14 terms
Law of Sines VS. Law of Cosines
Law of Cosines (finding sides)
Law of Cosines (finding angles)
Law of Sines (finding angles)
Law of Sines (finding sides)
Law of Cosines (finding sides)
Law of Cosines (finding angles)
14 terms
Law of Sines and Cosines
oblique triangle
Law of sines is used to solve...
Law of sines
what letters mean what in labeling a t…
a triangle that does not have a right angle
ASA, AAS, SSA
a/sinA = b/sinB = c/sinC
lowercase means side and capital is an angle
oblique triangle
a triangle that does not have a right angle
Law of sines is used to solve...
ASA, AAS, SSA
11 terms
Law of Sines and Cosines
Law of Sines
Area of a Triangle
Apothem
Law of Cosines
In any triangle, the ration between the sine of any angle and…
To find the area of any triangle, we take half the product of…
segment from the center of the polygon perpendicular to the s…
a^2 = b^2 + c^2 - 2bc COSA
Law of Sines
In any triangle, the ration between the sine of any angle and…
Area of a Triangle
To find the area of any triangle, we take half the product of…
11 terms
Law of Sines and Cosines
a/sina = b/sinb = c/sinb
height is bigger than side oposite
height = the side oposite
opposite side is bigger than height an…
law of sines
no solution
1 right triangle
1 solution
a/sina = b/sinb = c/sinb
law of sines
height is bigger than side oposite
no solution
15 terms
Math law of sines/cosines
Given SSS or SAS
After using LOC, solve for ______ with…
Area of triangle
Law of sines
Law of cosines... a^2 = b^2+c^2-2bccosA ... b^2 = a^2+c^2-2accosB…
Smallest angle
1/2•base•height
sin A/a =sin B/b = sin C/c
Given SSS or SAS
Law of cosines... a^2 = b^2+c^2-2bccosA ... b^2 = a^2+c^2-2accosB…
After using LOC, solve for ______ with…
Smallest angle
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