Question

Sam is at the top of a tower and will ride down a zip line to a lower tower. The total vertical drop of the zip line is 40 ft. The zip lines angle of elevation from the lower tower is LaTeX: 15^\circ.15 ∘ . What is the horizontal distance between the two towers? Round your answer to the nearest hundredth. Group of answer choices

Answer 1

149.30ft

Explanation:

Since the vertical distance between the two tower = 40ft

The angle of elevation from the lower tower to te higher tower = 15°

The horizontal distance between the two towers = x

Assuming the angle of elevation and the distance between the two towers makes a right angle triangle, we can use SOHCAHTOA and determine which one would be suitable to find x.

Check attached document for better illustration of the triangle.

Tanθ = opposite / adjacent

Opposite = 40

θ = 15°

Adjacent = x

Tan15 = 40 / x

0.2679 = 40 / x

X = 40 / 0.2679

X = 149.30ft

The horizontal distance between the two towers is 149.30ft