Basic Trigonometry Review

Pythagorean Theorem

100

What is the equation of the Pythagorean Theorem?

a²+b²=c²

200

If the hypotenuse has a length of 25 and one leg has the length of 7, what is the length of the other leg?

The length is 24.

300

The side lengths of a triangle are 15, 20, and 25. Is this triangle a right triangle?

Yes by the converse of the Pythagorean Theorem.

400

The side lengths of a triangle are 0.3, 0.4, and 0.6. Does this make a right triangle?

No, the Pythagorean Theorem does not work.

500

If the length of the hypotenuse is 5 square root 6 and the length of one leg is 10 , what is the length of the other leg?

5 square root 2 or square root of 50.

Special Right Triangles

100

How are the side lengths of a 45˚-45˚-90˚ triangle related?

x : x : x square root 2

200

How are the side lengths of a 30˚-60˚-90˚ triangle related?

x : x square root 3 : 2x

300

If the hypotenuse of 45˚-45˚-90˚ triangle is 10, what are the legs of the triangle?

5 square root of 2

400

If the leg opposite of the 60˚ side has length 9, what are the lengths of the other two sides?

3 square root 3, 6 square root 3.

500

If the hypotenuse of a 30˚-60˚-90˚ triangle is 18, what are the lengths of the other two sides?

9, 9 square root 3.

Simplifying Radicals

100

What is the square root of 121?

11

200

Simplify the square root of 50

5 square root 2

300

Simplify the square root of 300

10 square root 3

400

Simplify the square root of 98

7 square root 2

500

Simplify square root of 96

4 square root 6

Trigonometric Ratios

100

What is the definition of cosine?

cos(theta) = Adjacent / Hypotenuse

200

For angle X, the sides of a triangle are A = 3, O = 4, and H = 5. What is tan(H)?

tan(H) = 4 / 3

300

For angle F, the sides are A = 15 , O = 8, and H = 17. What is tan(F)?

tan(F) = 8 / 15

400

For angle T, if A = 3, O = 4, then what is cos(T)?

cos(T) = 3 / 5

500

For angle L, if A = 6 and O = 8, what is sin(L)?

sin(L) = 8 / 10 or 4 / 5

Angles in Triangles

100

What operation is used to find the angle K if cos(K) = 2 / 1?

Inverse cos or cos^-1

200

For angle X, if O = 20, and H = 35, what is the measure of angle X?

34.8˚

300

For angle C, if A = 6 and H = 15, what is the measure of angle C?

66.4˚

400

For angle B, A = 16, O = 30, H = 34, what is the measure of angle B?

61.9˚

500

For angle W, A = 6, O = 8, H = 10, what is the measure of angle W?

53.1˚