Question

The top of a 230 foot vertical tower is to be anchored by cables that make an angle with a measure of 50 degrees with the ground.

How long must each cable be? ____ feet   
How far from the base of the tower should the anchors be placed? _____ feet   
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Answer 1

9514 1404 393

Answer:

• cable length: 300.2 ft
• anchor distance: 193.0 ft

Explanation:

The side given is opposite the given angle. We want to find both the hypotenuse and the adjacent side in the right triangle that models the geometry.

Sin = Opposite/Hypotenuse

sin(50°) = (230 ft)/h

h = (230 ft)/sin(50°) ≈ 300.24 ft

The length of the cable must be about 300.2 feet.

__

Tan = Opposite/Adjacent

tan(50°) = (230 ft)/d

d = (230 ft)/tan(50°) ≈ 192.99 ft

The cable must be anchored about 193.0 ft from the tower.