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Geometry Chapter 7 Right Triangles Flashcards

Flashcards for McDougal Littell Geometry Chapter 7 Right Triangles
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Pythagorean Theorem
In a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2
Obtuse triangle
In a triangle with shorter sides a and b and longer side c, if a^2 + b^2 < c^2, then the triangle is obtuse
Acute triangle
In a triangle with shorter sides a and b and longer side c, if a^2 + b^2 > c^2, then the triangle is acute
Pythagorean Triple
Three positive integers that satisfy a^2 + b^2 = c^2, that is, they could be the three side lengths of a right triangle. Primitive triples include: 3, 4, 5; 5, 12, 13, and 8, 15, 17. More triples can be formed by multiplying each member of a primitive triple by the same multiplier; for example, since 3, 4, 5 is a triple, so is 6, 8, 10.
45-45-90 right triangle
Special right triangle: isosceles right triangle where the legs are congruent and the hypotenuse = leg * sqrt(2)
30-60-90 right triangle
Special right triangle: hypotenuse = shorter side 2; longer side = shorter side sqrt(3)
sine
trigonometric ratio: abbreviation sin; the sine of an acute angle in a right triangle equals the side opposite the angle divided by the hypotenuse (sin A = opp/hyp)
cosine
trigonometric ratio: abbreviation cos; the cosine of an acute angle in a right triangle equals the side adjacent to the angle divided by the hypotenuse (cos A = adj/hyp)
tangent
trigonometric ratio: abbreviation tan; the tangent of an acute angle in a right triangle equals the side opposite the angle divided by the adjacent side (tan A = opp/adj)
SOH CAH TOA
Mnemonic device to help remember the trig ratios in a right triangle: sin = opp/hyp; cos = adj/hyp; tan = opp/adj
Inverse Trig Ratio
Gives us the measure of the angle whose sin/cos/tan is a given ratio value. "Undoes" sin, cos, or tan. Written using a "-1" (looks like an exponent, but isn't). Also called "arc," such as arcsin, arccos, arctan. Example: arcsin(1/2) = 30 degrees. Useful in finding missing angle values in right triangles.
trigonometric ratios
Ratios formed by the sides of a right triangle. Useful in finding the missing sides of a right triangle given an angle and a side. Trigonometric ratios include sine (sin), cosine (cos), and tangent (tan). Other ratios (not covered in this chapter) are: cosecant, secant, and cotangent
Solve a triangle
Means finding any missing angles and/or sides in a triangle. Methods to solve a right triangle include the Pythagorean theorem, triangle sum theorem (if given one acute angle in a right triangle, we can find the other by subtracting the acute angle's measure from 90), trig ratios, and inverse trig functions
Angle of elevation
The angle formed when looking up from the horizontal
Angle of depression
The angle formed when looking down from the horizontal