Math Word Problem: Trigonometry

Question

A lifeguard spots a swimmer in the lake at an angle of depression of 45°. He spots a sailboat, further out, at an angle of depression of 26°. If the lifeguard is 36.5 dm away from the swimmer and 84.7 dm away from the sailboat, how far is the swimmer from the sailboat?

Answer 1

You have to draw a picture to really understand....

 

There are 2 right triangles in quadrant 4

 

The first right triangle is formed by the lifeguard and the swimmer.

It is in fact, 45-45-90 right triangle

 

The second right triangle is formed by the lifeguard and the sailboat.

THe angles are 26 and 64 degrees 

 

 

The HYPOTENUSES of both right triangles are 36.5 and 84.7 as given in the problem

 

 

The portion of the x-axis with respect to the first right triangle is found as

 

   cos 45 = x/36.5

   x = 36.5 * cos 45 = 36.5 * sqrt(2)/2 = 25.809

 

The portion of the x-axis with respect to the second right triangle is found as

 

   cos 26 = x/84.7

  x = 84.7 * cos 26 = 76.128

 

The distance between the swimmer and the sailboat is 76.128-25.809 = 50.32 correct to 2 digits