Chapter 11: Right Triangles & Trigonometry

Question 1

Theorem 56: The altitude to the hypotenuse of a right triangle forms

Answer 1

two triangles that are similar to each other and to the original triangle

Question 2

Theorem 57: The Pythagorean Theorem: The square of the length of the hypotenuse of a right triangle is

Answer 2

equal to the sum of the squares of the lengths of the lengths of the legs

Question 3

Theorem 58: Converse of the Pythagorean Theorem: If the square of one side length of a triangle is equal to the sum of the squares of the other two side lengths, then

Answer 3

the triangle is a right triangle

Question 4

Theorem 59: In an isosceles right triangle, the length of the hypotenuse is

Answer 4

√2 times the length of one leg

Question 5

Theorem 60: In a 30-60 right triangle, the length of the hypotenuse is

Answer 5

twice the length of the short leg and the length of the long leg is √3 times the length of the short leg

Question 6

The tangent ratio is

Answer 6

the ratio of the length of the opposite side to the length of the adjacent side of a right triangle, with respect to a given angle: tan = opp/adj

Question 7

The sine ratio is

Answer 7

the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle, with respect to a given angle: sin = opp/hyp

Question 8

The cosine ratio is

Answer 8

the ratio of the length of the adjacent side to the length of the hypotenuse of right triangle, with respect to a given angle: cos = adj/hyp