Trigonometry Real-World Applications 2 — Questions and Answers
Question 1: A ship's navigator uses radar to detect an obstacle at a bearing of N 35° E and a distance of 12 nautical miles. How far north of the ship is the obstacle?
- 9.83 nautical miles (Correct answer)
- 6.88 nautical miles
- 10.24 nautical miles
- 7.53 nautical miles
Correct answer: 9.83 nautical miles
The northward distance is 12 × cos(35°) ≈ 12 × 0.819 ≈ 9.83 nautical miles.
Question 2: A Ferris wheel has a radius of 25 feet and its center is 30 feet above the ground. A rider starts at the bottom. After rotating 120°, what is the rider's height above the ground?
- 42.5 feet (Correct answer)
- 55 feet
- 17.5 feet
- 30 feet
Correct answer: 42.5 feet
Height = 30 + 25 × sin(120° − 90°) = 30 + 25 × sin(30°) = 30 + 12.5 = 42.5 feet.
Question 3: A contractor needs to build a ramp with a 7° incline to cover a horizontal distance of 20 feet. What is the length of the ramp surface?
- 20.15 feet (Correct answer)
- 18.73 feet
- 21.40 feet
- 19.68 feet
Correct answer: 20.15 feet
Ramp length = 20 / cos(7°) ≈ 20 / 0.9926 ≈ 20.15 feet.
Question 4: Two forces of 80 N and 60 N act on an object at an angle of 90° to each other. What is the magnitude of the resultant force?
- 100 N (Correct answer)
- 140 N
- 70 N
- 120 N
Correct answer: 100 N
For perpendicular forces, the resultant = √(80² + 60²) = √(6400 + 3600) = √10000 = 100 N.
Question 5: A surveyor stands at point A and measures an angle of elevation of 28° to the top of a hill. Standing 150 feet closer at point B, the angle of elevation is 42°. What is the height of the hill (to the nearest foot)?
- 183 feet (Correct answer)
- 210 feet
- 156 feet
- 230 feet
Correct answer: 183 feet
Using two angle-of-elevation equations: h = 150 × tan(28°) × tan(42°) / (tan(42°) − tan(28°)) ≈ 183 feet.
Question 6: A pendulum 1.5 meters long swings with a maximum angle of 10° from vertical. What is the maximum horizontal displacement of the bob?
- 0.261 meters (Correct answer)
- 0.148 meters
- 0.302 meters
- 0.197 meters
Correct answer: 0.261 meters
Horizontal displacement = 1.5 × sin(10°) ≈ 1.5 × 0.1736 ≈ 0.261 meters.
Question 7: An airplane flying at 5,000 feet altitude begins its descent at a 3° glide slope angle. How far (horizontal distance) from the runway threshold should the descent begin?
- 95,500 feet (Correct answer)
- 75,200 feet
- 110,000 feet
- 85,900 feet
Correct answer: 95,500 feet
Horizontal distance = 5000 / tan(3°) ≈ 5000 / 0.05241 ≈ 95,400 ≈ 95,500 feet.
Trigonometry Real-World Applications 2
A ship's navigator uses radar to detect an obstacle at a bearing of N 35° E and a distance of 12 nautical miles.
How far north of the ship is the obstacle?