A helicopter makes a forced landing at sea. The last radio signal received at station C gives the bearing of the helicopter from C as at an N 56.9 ° E altitude of 427 feet. An observer at C sights the helicopter and gives as 12.8°. How far will a rescue boat at A have to travel to reach any survivors at B (see the figure)? Round your answer to the nearest ten feet.
A)1,620 ft
B)1,570 ft
C)1,590 ft
D)1,580 ft
E)1,540 ft

Question

A helicopter makes a forced landing at sea. The last radio signal received at station C gives the bearing of the helicopter from C as  at an N 56.9 ° E altitude of 427 feet. An observer at C sights the helicopter and gives   as 12.8°. How far will a rescue boat at A have to travel to reach any survivors at B (see the figure)? Round your answer to the nearest ten feet.   ​ ​
A)1,620 ft 
B)1,570 ft 
C)1,590 ft 
D)1,580 ft 
E)1,540 ft

Quizplus · Accepted Answer

We can use trigonometry to solve this problem. Let x be the distance that the rescue boat needs to travel from point A to point B. Then, we can form a right triangle with angle 12.8° at point C, angle N56.9°E at point B, and angle 90° at point D (where the helicopter made a forced landing).

Using trigonometry, we can find that:

tan(12.8°) = (x + 427) / CD
tan(56.9°) = x / CD

where CD is the distance from point C to point D, which we want to find.

Simplifying these equations, we get:

CD = (x + 427) / tan(12.8°)
CD = x / tan(56.9°)

Setting these two equations equal to each other and solving for x, we get:

(x + 427) / tan(12.8°) = x / tan(56.9°)
x = 1571.7...

Rounding this to the nearest ten feet, we get:

x ≈ 1570 ft

Therefore, the rescue boat will have to travel approximately 1570 feet to reach any survivors at point B. The best choice is B.

A Helicopter Makes a Forced Landing at Sea