Question

PLEASE HELP ME!

A support wire for a tower is connected from an anchor point on level ground to the top of the tower. The straight wire makes a 65 degree angle with the ground at the anchor point. At a point 25 meters farther from the tower than the wire's anchor point and on the same side of the tower, the angle of elevation to the top of the tower is 35 degrees. Find the wire length to the nearest tenth of a meter.

Answer 1

28.7 meters

Explanation:

Draw a diagram. Let's say d is the distance between the anchor and the bottom of the tower, h is the height of the tower, and x is the length of the wire.

Using trigonometry, we can write two equations for the height of the tower:

h = d tan 65°

h = (d + 25) tan 35°

Setting these equal, we can solve for d.

d tan 65° = (d + 25) tan 35°

d tan 65° = d tan 35° + 25 tan 35°

d (tan 65° − tan 35°) = 25 tan 35°

d = 25 tan 35° / (tan 65° − tan 35°)

d ≈ 12.12

Now we can find x:

cos 65° = d / x

x = d / cos 65°

x ≈ 28.7

The wire is approximately 28.7 meters long.