#### Study sets matching "law of sines sines cosines"

#### Study sets matching "law of sines sines 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…

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…

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°

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

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

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

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°

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…

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

Law of Sines is used for solving what…

Law of Cosines is used for what situat…

The ambiguous case for oblique triangl…

How can you use the Law of Sines to de…

have two angles, AAS or ASA

solve oblique triangles in which 2 sides and included angles…

when two sides and the unincluded angle are given, SSA

Use Law of Sines to find the missing angle. If the sine is gr…

Law of Sines is used for solving what…

have two angles, AAS or ASA

Law of Cosines is used for what situat…

solve oblique triangles in which 2 sides and included angles…

What is the law of sines?

What do you do when you are given two…

How do you find the area of an oblique…

What is the law of cosines?

You find the third angle. You use the angles to find the rest…

By using A=1/2bcsinA, and plugging in the right numbers!

It has different versions depending on what you need. ... a^2= b…

What is the law of sines?

What do you do when you are given two…

You find the third angle. You use the angles to find the rest…

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)

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

AAA

AAS

SSA

ASA

The lengths cannot be determined

Sum of angles is 180 to find the last angle, LOS for the rema…

LOS for the angle opposite smallest side. Sum of angles is 18…

Sum of angles is 180 to find the last angle, LOS for the rema…

AAA

The lengths cannot be determined

AAS

Sum of angles is 180 to find the last angle, LOS for the rema…

Law of cosines

Impt in strategy for SAS triangle

Step 1 for SAS triangle

Step 2 for SAS triangle

a2=b2+c2-2bc(CosA)

Never use LOS on the largest angle

use LOC to find 3rd side

use LOS to find 1 of remaining angles by using shorter side

Law of cosines

a2=b2+c2-2bc(CosA)

Impt in strategy for SAS triangle

Never use LOS on the largest angle

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

Law of sines

Law of cosines

Area formula

Heron's formula

sin(A)/a=sin(B)/b=sin(C)/c,works for ASS, SSA

c^2=a^2+b^2-2

**a**b*cosC works for SAS, SSSArea=1/2

**b**c*sinAArea=square root(s(s-a)(s-c)(s-b))

Law of sines

sin(A)/a=sin(B)/b=sin(C)/c,works for ASS, SSA

Law of cosines

c^2=a^2+b^2-2

**a**b*cosC works for SAS, SSSlaw of sines

Ambiguous Case

Area of Oblique Triangles

Law of Cosines (Standard)

a/sin A = b/sin B = c/sin C... sin A/a = sin B/b = sin C/c... -SAS…

a<h - none... a=h - one (90 degrees)... h<a<b - two... a>b - one (obtu…

Area=1/2(b)(c)(sinA) ... Area=1/2(a)(b)(sinC)... Area=1/2(a)(c)(sin…

a^2=b^2+c^2 - 2(b)(c)(cosA)... b^2=a^2+c^2 - 2(a)(c)(cosB)... c^2=a…

law of sines

a/sin A = b/sin B = c/sin C... sin A/a = sin B/b = sin C/c... -SAS…

Ambiguous Case

a<h - none... a=h - one (90 degrees)... h<a<b - two... a>b - one (obtu…

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)

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

SSS

SAS

SAA

SSA

Law of Cosines to find largest angle, Law of Sines

Law of Cosines, Law of Sines to find smaller angle

Subtract to find 3rd angle measure, Law of Sines

Ambiguous Case

SSS

Law of Cosines to find largest angle, Law of Sines

SAS

Law of Cosines, Law of Sines to find smaller angle