This problem involves a right triangle, where:

• The height of the telephone pole is 60 feet.
• The length of the guy wire is 87 feet.

We are asked to find the angle $\theta$ between the guy wire and the pole. This angle is located between the pole (the vertical side) and the guy wire (the hypotenuse).

To solve for $\theta$, we can use the sine function, since we know the opposite side (the height of the pole) and the hypotenuse (the length of the wire).

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{60}{87}$

Now, calculate $\theta$ by taking the inverse sine (arcsin):

$\theta = \sin^{-1}\left(\frac{60}{87}\right)$

$\theta \approx \sin^{-1}(0.6897) \approx 43.58^\circ$

Rounding to the nearest degree:

$\theta \approx 44^\circ$

Thus, the angle between the wire and the pole is approximately 44 degrees.

Would you like more details on the steps or have any questions? Here are some related questions:

1. How would you find the angle if the height of the pole changed?
2. What would the angle be if the guy wire was shorter or longer?
3. How does the sine function help in determining angles in right triangles?
4. What other trigonometric functions could be used to solve this problem?
5. How can the Pythagorean theorem verify the dimensions of this triangle?

Tip: The sine function is often useful when you know the opposite side and the hypotenuse in a right triangle.