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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)

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 class=

Respuesta :

Kalahira
First draw a right triangle

       The building is the vertical leg and the shadow is the horizontal leg

   the hypotenuse makes a 20 degree angle with the top of the building

   call the shadow "x"

       tan=opposite/ adjacent

   tan(20Âş)=150/x

   x=150/tan(20Âş)

   x=150/0.36397

   x=412.121

       Therefore the answer is 412 Feet
kudzordzifrancis
ANSWER

The length of the shadow is
[tex]412ft.[/tex]

EXPLANATION

The shadow cast by the building is
[tex]b \: ft[/tex]
long.

We use trigonometry to determine the length of b.

[tex]b[/tex]
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.

[tex] \tan(20 \degree) = \frac{length \: of \: opposite \: side}{length \: of \:adjacent\: side} [/tex]

[tex]\Rightarrow \: \tan(20 \degree) = \frac{150ft} {b \: ft}[/tex]

[tex]\Rightarrow \: b = \frac{150} {\tan(20 \degree)}[/tex]

[tex]\Rightarrow \: b = 412.122ft[/tex]

To the neatest feet,the length of the shadow is

[tex]412ft.[/tex]

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