Question

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A 103-foot wire is used to support a utility tower. It runs from the tower to the ground and forms a 24° angle with the ground.

Answer 1

Answer:

Height of Tower = 41.8901 ft

Base to Ground Wire = 94.0905 ft

Step-by-step explanation:

So you want to find the opposing side of the angle, as well as the distance from the base to where the wire is attached to the ground. You would need to use CAH to find the ground, and SOH to find the height. To find the height or opposite, take the Sine of 24°, 0.4067, and times it by your hypoteneuse 103 to get an exact height of 41.8901 ft. Next, use the Cosine of 24°, 0.9135, and times that by your hypoteneuse 103 to get 94.0905 ft.

Here are the equations:

sin(24)=$\frac{h}{103}$

cos(24)=$\frac{h}{103}$

Answer 2

The base of the utility tower from the location where wire is attached to the ground is 94.09 feet and the wire attached to the tower at a height of 41.89 feet.

What is right angle triangle property?

In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.

$\cos\theta=\dfrac{a}{c}$

Here, (a) is the adjacent side, (c) is the hypotenuse side and $\theta$ is the angle made between them.

• a) The value from the base of the utility tower from the location where wire is attached to the ground

The length of the wire is 103 foot. This is the hypotenuse side of triangle made by the wire, tower, and ground.

The angle between the wire (hypotenuse side) and ground (adjacent side) is 24 degrees. Therefore, the cosine angle can be given as,

$\cos (24^o)=\dfrac{a}{103}\\0.9135\times103=a\\a=94.09\rm ft$

• b) The wire attached to the tower at a height of __ feet.

In a right angle triangle ratio of opposite side to the hypotenuse side is equal the sine angle between them. Let the height of the tower (opposite side) is b ft. Therefore,

$\sin(24^o)=\dfrac{b}{103}\\0.4067\times103=b\\b=41.89\rm ft$

Thus, the value from the base of the utility tower from the location where wire is attached to the ground is 94.09 feet and the wire attached to the tower at a height of 41.89 feet.

Learn more about the right angle triangle property here;

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