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
How long must each cable be? ____ feet
How far from the base of the tower should the anchors be placed? _____ feet
1 answer:
9514 1404 393
Answer:
- cable length: 300.2 ft
- anchor distance: 193.0 ft
Step-by-step 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.
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