Question

An h = 135-ft tower is located on the side of a mountain that is inclined 32° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire needed. (Round your answer to the nearest foot.)

Answer 1

Answer:

171 foot

Step-by-step explanation:

We are given that

Height of tower=135 ft

AC=55 ft

Let x be the length of shortest length of wire.

The angle of inclination of mountain with horizontal =$32^{\circ}$

The angle between sides AB and BC=$90+32=122^{\circ}$

Exterior angle is equal to sum interior angles of a triangle on the opposite sides .

We have to find the value of x.

We know that law of cosine

$c=\sqrt{a^2+b^2-2ab cos\theta}$

Substitute the values in the given formula we get

$x=\sqrt{(135)^2+(55)^2-2(135)(55)cos 122}$

$x=170.64 ft$

Hence, the length of wire needed=171 foot