Questions: When the angle of elevation of the sun is 68°, a telephone pole that is tilted at an angle of 8° directly away from the sun casts a shadow 24 feet long. Determine the length of the pole to the nearest foot. The length of the pole is ft (Type an integer.)

When the angle of elevation of the sun is 68°, a telephone pole that is tilted at an angle of 8° directly away from the sun casts a shadow 24 feet long. Determine the length of the pole to the nearest foot.

The length of the pole is ft
(Type an integer.)

Transcript text: When the angle of elevation of the sun is $68^{\circ}$, a telephone pole that is tilted at an angle of $8^{\circ}$ directly away from the sun casts a shadow 24 feet long. Determine the length of the pole to the nearest foot. The length of the pole is $\square$ ft (Type an integer.)

Solution

Solution Steps

Step 1: Find the height of the right triangle formed by the shadow.

The shadow forms the base of a right triangle, with length 24 feet. The angle of elevation of the sun is 68°. Let 'h' be the height of this triangle. We can use the tangent function to relate the angle, base, and height:

tan(68°) = h / 24

h = 24 * tan(68°) ≈ 24 * 2.475 ≈ 59.4

Step 2: Find the length of the pole.

The height 'h' calculated in the previous step is the adjacent side to the 8° angle formed by the tilted pole and the vertical. The pole's length, 'b', is the hypotenuse of this triangle. We can use the cosine function to relate these:

cos(8°) = h / b

b = h / cos(8°) ≈ 59.4 / 0.990 ≈ 60