Find the length of the angle

Question

In a 58° - 32° right triangle, the side adjacent to the 32° angle is 41.74 inches. If tan58° = 1.6003, find the length of the side opposite the 32° angle. Estimate your answer to 3 decimal places.

Answer 1

tan 58 = 41.74/x

x=41.74/1.6003

 = 26.0777 inch

=26.088inch

 

Answer 2

The side adjacent to the 32° angle is also the side opposite to the 58° angle.  Let x be the side adjacent to the 58° angle.  

 

Then, tan58° = opposite/adjacent = 41.74/x = 1.6003

 

                     So, x = 41.74/1.6003 ≈ 26.083