Question

A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower. The wire makes an angle of 65° with the ground. Draw a diagram and find the length of the guy wire. 4.2 yd. 11.0 yd. 23.7 yd.

Answer 1

23.7 yards

Explanation:

Given :A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower. The wire makes an angle of 65° with the ground

To Find: Draw a diagram and find the length of the guy wire

Solution :

Refer the attached figure

We are given that A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower i.e. AC = 10 yards

We are also given that wire makes an angle of 65° with the ground i.e. ∠BAC = 65°

Now to find the length of the guy wire i.e. AB

We will use trigonometric ratio.

`cos\theta = (Base)/(Hypotenuse)`

`cos 65 ^(\circ) = (AC)/(AB)`

`0.4226= (10)/(AB)`

`AB= (10)/(0.4226)`

`AB= 23.66`

Thus AB = 23.66 yards ≈ 23.7 yards

Hence the length of the guy wire is 23.7 yards

Answer 2

The wire, the tower and the ground will make a right triangle with hypotenuse that is equal to the length of the wire, the height that is equal to the height of the tower and the base that measures from the base of the building to point the wire has touched the ground.
The length of the wire will be given by:
cos θ = (adjacent)/(hypotenuse)
thus
cos 65=10/h
h=10/cos 65
h=23.66 yds~23.7 yds
the answer is 23.7 yd