A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 65°. A guy wire is to be attached to the top of the tower and to the ground, 148 ft downhill from the base of the tower. The angle formed by the guy wire is 9°. Find the length of the cable required for the guy wire.

PLEASE I JUST NEED THE ANSWER!!!

sorry - you will have to do some work, too ...

Draw a diagram and label
A = place where guy wire meets the hill
P = point level with A, just below the tower
T = top of tower
Now you can see that
AP/148 = cos65°
AP/AT = cos74°
You want the distance AT

To find the length of the cable required for the guy wire, we can use trigonometry. Let's break down the steps to get the answer:

1. First, draw a diagram to visualize the situation. Make sure to label all the given information. In this case, draw a triangle representing the hill, the tower, and the guy wire.

2. Label the angle of inclination of the hill as 65° and the angle formed by the guy wire as 9°.

3. We know that the guy wire is attached to the top of the tower and the ground 148 ft downhill from the base of the tower. Mark this distance on your diagram.

4. Now, trigonometry comes into play. The angle of inclination (65°) can be used to find the height of the hill. We can use the sine function: sin(65°) = opposite/hypotenuse. The opposite side is the height of the hill, and the hypotenuse is the distance between the base of the tower and the guy wire. Let's call this distance 'x'.

sin(65°) = height/x

Rearranging the equation, we get: height = x * sin(65°)

5. We also know that the angle formed by the guy wire is 9°. We can use the sine function again to find the length of the guy wire. The opposite side is the height we just calculated, and the hypotenuse is the length of the guy wire. Let's call this length 'y'.

sin(9°) = height/y

Rearranging the equation, we get: y = height / sin(9°)

6. Substitute the value of height from step 4 into the equation in step 5:

y = (x * sin(65°)) / sin(9°)

7. Now, we need to find the value of 'x'. The distance between the base of the tower and the guy wire is 148 ft. We can use the cosine function to relate the angle of inclination (65°) and the length of 'x'. The cosine function states: cos(65°) = adjacent/hypotenuse. The adjacent side is 'x', and the hypotenuse is 148 ft.

cos(65°) = x/148

Rearranging the equation, we get: x = 148 * cos(65°)

8. Substitute the value of 'x' from step 7 into the equation in step 6:

y = ((148 * cos(65°)) * sin(65°)) / sin(9°)

9. Now, calculate the value of 'y' using a calculator or appropriate software:

y ≈ 154.43 ft

So, the length of the cable required for the guy wire is approximately 154.43 ft.