A communication tower is supported by several guy wires. If the guy wires are placed 32 feet from the base of the tower and for a 71 degree angle with the ground. How long does each wire need to be rounded to the nearest tenth.
Write the equation, and show all your work to solve for the indicated length.
To solve this problem, we can use trigonometric ratios. In this case, we can use the tangent ratio (tan).
Let's denote the length of each guy wire as "x". The angle formed between the guy wire and the ground is given as 71 degrees.
From the given information, we know that the distance from the base of the tower to the guy wire is 32 feet. We can label this as the opposite side (O) in our trigonometric ratio. The unknown length of the guy wire (x) is the adjacent side (A) in our trigonometric ratio.
The tangent ratio is defined as:
tan(angle) = O/A
Substituting in the given values:
tan(71°) = 32/x
To solve for x, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by x:
x * tan(71°) = 32
Finally, solving for x, we divide both sides of the equation by tan(71°):
x = 32 / tan(71°)
Using a calculator, we find:
x ≈ 32 / 2.917 ≈ 10.99 feet
Therefore, each guy wire needs to be rounded to the nearest tenth and is approximately 11 feet in length.