A guy wire makes a 67° angle with the ground. Walking out 32 feet further from the tower, the angle of elevation to the top of the tower is 39°. Find the height of the tower.

This is the theory of geometry, the height of the tower will be given by:

tan theta=[opposite]/[adjacent]

let the opposite be h;

adjacent be x;

tan 67=h/x

thus;

h=xtan67

also

tan39=h / (x+32)

h = (x+32) tan39

xtan67 = (x+32) tan39

2.4x = (x+32) 0.8

2.4x=0.8x+25.6

2.4x-0.8x=25.6

1.6x=25.6

x=25.6/1.6

x=16 ft

thus

h=xtan67

h=16tan67

h=37.7 ft