Question

A guy wire to a tower makes a 71° angle with level ground. At a point 36 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 36°. Find the length of the wire (to the nearest foot). *

Answer 1

The length of the wire is 37.15 ft

Explanation:

The figure is attached for the reference.

tan (71) = $\frac{y}{x}$

tan (36) = $\frac{y}{36+x}$

So,

tan(36) (36 + x) = y

tan(71) = $\frac{tan (36) (36 + x )}{x}$

$2.9 = \frac{0.73 (36 + x)}{x} \\\\2.9 x = 26.28 + 0.73x\\\\2.17x = 26.28\\\\x = 12.11 ft$

Substituting x = 12.11 ft in equation 1:

$tan (71) = \frac{y}{12.11} \\\\2.9 X 12.11 = y\\\\y = 35.119 ft$

Length of the wire, z = $\sqrt{x^2 + y^2}$

So,

$z = \sqrt{(12.11)^2 + (35.119)^2} \\\\z = \sqrt{146.6521 + 1233.3442} \\\\z = 37.15 ft$

Therefore, the length of the wire is 37.15 ft