Question

The angle of depression from the top of apartment building to the base of fountain in a nearby park is 72 degree s. if the building is 78 feet tall. how far away is the fountain?

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

The fountain is $25.34\text{feet}$ far.

Step-by-step explanation:

Given: The angle of depression from the top of apartment building to the base of fountain in a nearby park is $72^\circ$ & height of building is 78 feet.

To find: distance of fountain.

Refer figure below for further calculation.

By figure, $\angle{ABC}=72^\circ$ (Alternating angle), $AC=78 feet$.

To find $AB$

Using $tan\theta=\frac{AC}{AB}$ we have:

$tan72^\circ=\frac{78}{AB}$

    $AB=\frac{78}{tan72^\circ}$

    $AB=\frac{78}{3.078}$    

    $AB=25.34\text{feet}$

So, the fountain is $25.34\text{feet}$ far.

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