Mathematics: Consider the diagram shown where the sun is 20° above the horizon. how long is the shadow cast by a building 150 ft tall? (to the nearest ft)

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Consider the diagram shown where the sun is 20° above

Ответ:

tdun7003

09.01.2022

Mathematics

ANSWER

The length of the shadow is
412ft.

EXPLANATION

The shadow cast by the building is
$b \: ft$
long.

We use trigonometry to determine the length of b.

is the length of the side that is adjacent to the 20° angle.

We also know the length of the side that is opposite to the 20° angle to be 150ft.

We now use the tangent ratio to determine the value of b.

$\tan(20 \degree) = \frac{length \: of \: opposite \: side}{length \: of \:adjacent\: side}$

$\Rightarrow \: \tan(20 \degree) = \frac{150ft} {b \: ft}$

$\Rightarrow \: b = \frac{150} {\tan(20 \degree)}$

$\Rightarrow \: b = 412.122ft$

To the neatest feet,the length of the shadow is

412ft.

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Consider the diagram shown where the sun is 20° above the horizon. how long is the shadow cast by a building 150 ft tall? (to the nearest ft)

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