Questions: Reuben attached a wire between two poles on a hill as shown. Which is closest to x, the distance between the two poles? (1) 60 ft (9) 27 ft (11) 75 ft (1) 29 ft

Reuben attached a wire between two poles on a hill as shown.

Which is closest to x, the distance between the two poles?
(1) 60 ft
(9) 27 ft
(11) 75 ft
(1) 29 ft

Transcript text: Reuben attached a wire between two poles on a hill as shown. Which is closest to $x$, the distance between the two poles? (1) 60 ft (9) 27 ft (11) 75 ft (1) 29 ft

Solution

Solution Steps

Step 1: Identify the given information

We are given a triangle formed by the wire and the horizontal distance between the poles. The wire's length is 80 ft. The angle between the wire and the horizontal is 20°. We need to find the horizontal distance _x_.

Step 2: Choose the appropriate trigonometric function

Since we have the hypotenuse (80 ft) and we're looking for the adjacent side (_x_) with respect to the given angle (20°), we should use the cosine function.

Step 3: Set up the equation and solve

cos(20°) = adjacent/hypotenuse = x/80

x = 80 * cos(20°)

x ≈ 80 * 0.9397

x ≈ 75.18 ft