Trigonometry Right Triangle Solutions 2

Question 1

In a right triangle, the two legs measure 9 and 40. What is the length of the hypotenuse?

Accepted Answer

41

Answer

Using the Pythagorean theorem: √(9² + 40²) = √(81 + 1600) = √1681 = 41.

Question 2

A right triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg?

Accepted Answer

12

Answer

Using the Pythagorean theorem: √(13² − 5²) = √(169 − 25) = √144 = 12.

Question 3

In a right triangle with legs 7 and 24, what is the sine of the angle opposite the leg of length 7?

Accepted Answer

7/25

Answer

The hypotenuse is 25 (since 7² + 24² = 625 = 25²), and sin = opposite/hypotenuse = 7/25.

Question 4

If angle B in a right triangle is 52° and the hypotenuse is 20, what is the length of the side adjacent to angle B?

Accepted Answer

20 cos 52°

Answer

The adjacent side equals hypotenuse × cos(B) = 20 cos 52°.

Question 5

A ladder 15 ft long leans against a wall, making a 70° angle with the ground. How high up the wall does the ladder reach?

Accepted Answer

15 sin 70°

Answer

The height equals 15 sin 70° because the wall side is opposite the 70° angle.

Trigonometry Practice Test