Solve the word problem

Question

A guy wire to a tower makes a 65 degree angle with level ground. At a point 39 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the tower is 38 degrees. Find the length if the wire ( nearest foot).

Answer 1

H = height of the tower

L = length of the guy wire

sin(65 ) = H / L

H = L*sin(65)

 

Add 39 ft to L, and the angle is now 38 deg.,  so:

sin(38) = H / (L + 39)

 

Using the 1st equation, substitute for H:

sin(38) = L* sin(65) / (L + 39)

 

Plug in numbers and rearrange

0.616 = L*0.906 / (L + 39)

0.616*L + 24.0 = 0.906*L

0.29*L = 24.0

L = 83 feet

 

CHECK:

H = 83*sin(65) = 75

H = (83 + 39)*sin(38) = 75   OK!!!