The sun is 25° above the horizon. Find the length of a shadow cast by a building that is 100 feet tall. (Round your answer to two decimal places.)

Question

• Need answer in feet

Answer 1

Draw a right triangle with the right angle at the lower left corner.  The height of this triangle (the height of the building) is 100 and the base (the length of the shadow) is x.

 

The angle at the right is 25 degrees.

 

Since we are dealing with the sides opposite and adjacent to the 25 degree angle, we can solve for x using the tangent ratio.

 

tangent = opposite/adjacent  (Remember the TOA in SOHCAHTOA)

 

tan 25 = 100/x

 

0.4663 = 100/x

 

x = 100/0.4663 = 214.45

 

Answer 2

With 25 degree of elevation the rays of the sun will make that same angle with the ground

 

Let the length of the shadow be L

 

100/L = Tan 25 (Tan = opposite side/adjacent side)

 

L = 100/Tan 25 = 100/0.466 = 214.45 feet