Trigonometry Real-World Applications 5

Question 1

A golfer hits a ball at 45 m/s at an angle of 35° above horizontal. What is the vertical component of the initial velocity?

Accepted Answer

25.8 m/s

Answer

Vertical component = 45 × sin(35°) ≈ 45 × 0.5736 ≈ 25.8 m/s.

Question 2

An antenna must be guyed with a wire attached 30 feet up the mast and anchored 18 feet from the base. What angle does the guy wire make with the ground?

Accepted Answer

59.0°

Answer

Angle = arctan(30/18) = arctan(1.667) ≈ 59.0°.

Question 3

A marine biologist models the depth of a diving submarine as d(t) = 200 − 150 cos(π t / 10) feet, where t is minutes. What is the maximum depth reached?

Accepted Answer

350 feet

Answer

Maximum depth occurs when cos(πt/10) = −1, giving d = 200 − 150(−1) = 200 + 150 = 350 feet.

Question 4

A wheelchair ramp must have a maximum incline angle of 4.76°. What is the minimum horizontal length needed for a ramp rising 1.5 feet?

Accepted Answer

18.0 feet

Answer

Horizontal length = 1.5 / tan(4.76°) ≈ 1.5 / 0.0833 ≈ 18.0 feet (ADA standard: 1:12 ratio).

Question 5

A hiker walks 5 km due north, then turns and walks 8 km on a bearing of 060°. How far is the hiker from the starting point?

Accepted Answer

11.4 km

Answer

Using the Law of Cosines with the angle between the paths = 60°: d² = 5² + 8² − 2(5)(8)cos(120°) = 25 + 64 + 40 = 129; d ≈ 11.4 km.

Trigonometry Practice Test

Trigonometry Practice Test

Trigonometry Real-World Applications 5