Question

A ship in distress fires a signal flare. The flare explodes at a height of 800 feet above the ship. A rescue ship sees the flare and measures the angle of elevation from its location up to the flare to be about 16.0°. About how far is the ship that is in distress from the rescue ship?

a) Approximately 2920 feet
b) Approximately 1937 feet
c) Approximately 3080 feet
d) Approximately 2146 feet

Answer 1

To find the distance between the ship in distress and the rescue ship, we can use trigonometry. The ship in distress is approximately 2920 feet away from the rescue ship.

Step-by-step explanation:

To find the distance between the ship in distress and the rescue ship, we can use trigonometry. We have the height of the flare, 800 feet, and the angle of elevation, 16.0°. Let's assume that the distance between the two ships is x feet. Using the tangent function, we can set up the following equation:

tan(16.0°) = 800 / x

Solving for x, we find that x ≈ 2920 feet. Therefore, the ship in distress is approximately 2920 feet away from the rescue ship.