Question

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)

Answer 1

ANSWER

The length of the shadow is

`412ft.`

Step-by-step explanation

The shadow cast by the building is

`b \: ft`
long.

We use trigonometry to determine the length of b.


`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) = (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.`

Answer 2

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