2. A telephone pole support must hit the ground at an $55^{\circ}$ angle. If the telephone pole is 25 feet tall, hovt long is the wire that supports the pole? Round your answer to the nearest hundredth. (3 points)
Answer
\(\boxed{\text{Final Answer: The length of the wire that supports the pole is approximately 30.52 feet.}}\)
Step 1 ：Given a telephone pole of height 25 feet and a support wire that makes a $55^\circ$ angle with the ground, we need to find the length of the wire (L).
Step 2 ：Using the sine function, we can set up the equation: \(\sin(55) = \frac{25}{L}\)
Step 3 ：Solving for L, we get: \(L = \frac{25}{\sin(55)}\)
Step 4 ：Calculating the value of L, we find: \(L \approx 30.52\)
Step 5 ：\(\boxed{\text{Final Answer: The length of the wire that supports the pole is approximately 30.52 feet.}}\)
