Trigonometry Right Triangle Solutions 2 — Questions and Answers
Question 1: In a right triangle, the two legs measure 9 and 40. What is the length of the hypotenuse?
- 41 (Correct answer)
- 49
- 31
- 43
Correct answer: 41
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?
- 12 (Correct answer)
- 8
- 11
- 10
Correct answer: 12
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?
- 7/25 (Correct answer)
- 24/25
- 7/24
- 24/7
Correct answer: 7/25
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?
- 20 cos 52° (Correct answer)
- 20 sin 52°
- 20 tan 52°
- 20 / tan 52°
Correct answer: 20 cos 52°
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?
- 15 sin 70° (Correct answer)
- 15 cos 70°
- 15 tan 70°
- 15 / sin 70°
Correct answer: 15 sin 70°
The height equals 15 sin 70° because the wall side is opposite the 70° angle.
Question 6: In right triangle PQR with the right angle at R, if tan P = 3/4, what is sin P?
- 3/5 (Correct answer)
- 4/5
- 3/4
- 4/3
Correct answer: 3/5
With opposite = 3 and adjacent = 4, the hypotenuse = 5, so sin P = 3/5.
Question 7: A right triangle has an acute angle of 30°. If the side opposite the 30° angle is 8, what is the hypotenuse?
- 16 (Correct answer)
- 8√3
- 8√2
- 4
Correct answer: 16
Since sin 30° = 1/2, the hypotenuse = opposite / sin 30° = 8 / (1/2) = 16.
Trigonometry Right Triangle Solutions 2
In a right triangle, the two legs measure 9 and 40.
What is the length of the hypotenuse?