Questions: Solve the problem. A 140-ft tower is anchored on a hill by two guy wires. The angle of elevation of the hill is 8 degrees. Each guy wire extends from the top of the tower to a ground anchor 60 ft from the base of the tower and in line with the tower. Find the length of each guy wire. Round to the nearest foot.

Solution Steps

Since the angle of elevation is 8° and the horizontal distance from the base of the tower to each anchor is 60 ft, we can use the tangent function to find the elevated height (h) of each anchor: tan(8°) = h / 60 h = 60 * tan(8°) h ≈ 8.4 ft

Let's consider two right triangles: one formed by the tower, the ground, and the downhill wire (triangle 1), and the other by the tower, the ground, and the uphill wire (triangle 2). The length of the tower is 140 ft. The horizontal distance to each anchor point is 60ft and the elevated height of both anchor points are approximately 8.4ft

• Downhill wire: The effective height of the tower to the anchor is 140 ft + 8.4 ft = 148.4 ft. This forms the first leg of triangle 1. The horizontal distance of 60 ft is the second leg of triangle 1. Downhill wire length = √(148.4² + 60²) ≈ √(22022.56 + 3600) ≈ √25622.56 ≈ 160 ft

• Uphill wire: The effective height of the tower to the anchor is 140 ft - 8.4 ft = 131.6 ft. This forms the first leg of triangle 2. The horizontal distance of 60 ft is the second leg of triangle 2. Uphill wire length = √(131.6² + 60²) ≈ √(17318.56 + 3600) ≈ √20918.56 ≈ 145 ft

Final Answer: The downhill wire length is 160 ft and the uphill wire length is 145 ft. Note that these lengths have been rounded to the nearest foot as requested. None of the provided options are correct.