A boat has an angle of depression of 38° looking down to a submarine. The distance from the boat to the submarine is 500 yards. How far below sea level is the submarine?

307.8 yards

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Sin α = opposite side / hypotenuse  

Where α is the angle of depression of the boat looking down to a submarine, the hypotenuse is the distance from the boat to the submarine, and the opposite side (x) is the distance between the submarine and the sea level:

Replacing with the values given:  

Sin 38 = x/ 500

Solving for x  

Sin 38 (500) =x  

x= 307.8 yards

Feel free to ask for more if needed or if you did not understand something.  

faster, im not sure why but i know it is faster