Question

Samuel is at the top of the tower and will ride down a zip line to a lower tower. The total vertical drop of the zip line is 40ft. The zip line's angle of elevation from the lower tower is 11.5° . To the nearest tenth, what is the horizontal distance between the towers?

Answer 1

Answer:

196.6 feet

Step-by-step explanation:

Draw the right triangle formed by the zip-line.  Use SOH-CAH-TOA to write and solve an equation:

tan 11.5° = 40 / x

x = 40 / tan 11.5°

x = 196.6

Answer 2

The horizontal distance between the towers is 196.60 ft.

What are heights and distances in trigonometry?

Distance is the measurement of an object from a specific point in the horizontal direction, and height is the measurement of an object in the vertical direction.

Here, ∅₁ is called the angle of elevation and ∅₂ is called the angle of depression. For one specific type of problem in height and distances, we have a generalized formula. Height = Distance moved / [cot(original angle) – cot(final angle)] => h = d / (cot ∅₁ – cot ∅₂)

Given:

The vertical height of the zip line = 40 ft

The angle of elevation = 11.5°

We know, according to trigonometric values tan n = height / base

∴ tan 11.5 = 40 / base

base = 40/ tan 11.5

base = 40 / 0.203

base = 196. 60 ft

Therefore, the horizontal distance between the towers is 196.60 ft.

To learn more about heights and distances refer to :

https://brainly.com/question/17089830

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