Question

The sun is directly overhead. The shadow of the balloon falls

Answer 1

The height of the ballon is 34 feet 2 inches.

To be able to solve this question, we need to understand the concept of angle of elevation.

What is the angle of elevation?

An angle of elevation is the angle formed between the horizontal plane (adjacent line) to the line of sight(elevation) from the viewer's eye to the object located in the space.

• The diagrammatic expression for the question given can be seen in the image attached below.

From the image below, we can determine the height of the ballon by taking the tangential trigonometric function.

$\mathbf{tan \theta = \dfrac{opposite}{adjacent}}$

$\mathbf{tan \ 67= \dfrac{x}{14 ft \ 3 in }}$

Let's first convert 14 ft 6 in to ft, by doing so, we get 14.5 ft

$\mathbf{tan \ 67= \dfrac{x}{14.5\ ft }}$

x = tan 67 (14.5 ft)

x = 2.356(14.5 ft)

x =34.162 ft

To ft and inches, we have:

x = 34 ft 2 inches

Learn more about angles of elevation here:

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