Questions: A guy wire connects the top of a 128 foot tall cell tower to the ground. If the angle between the wire and the ground is 76 degrees, how long is the wire?
[?] feet
Round your answer to the nearest hundredth.
Transcript text: A guy wire connects the top of a 128 foot tall cell tower to the ground. If the angle between the wire and the ground is $76^{\circ}$, how long is the wire?
[?] feet
Round your answer to the nearest hundredth.
Solution
Solution Steps
Step 1: Calculate sin(76∘)
To find the length of the guy wire, we first need to calculate sin(76∘). The value obtained is:
sin(76∘)≈0.9703
Step 2: Use the Sine Function to Find the Length of the Wire
Using the sine function, we can relate the height of the tower to the length of the wire. The formula is given by:
hypotenuse=sin(θ)opposite
Substituting the known values:
hypotenuse=sin(76∘)128≈0.9703128≈131.92
Final Answer
The length of the wire is approximately:
131.92 feet