Question

Technology required. Jada is visiting New York City to see the Empire State building. She is100 feet away when she spots it. To see the top, she has to look up at an angle of86.1 degrees. How tall is the Empire State building?

Answer 1

Lets draw a picture of our problem

then, we have a right triangle

we can relate such quantities by means of the tangent function, that is,

`\tan 86.1=(h)/(100)`

by moving 100 to the left hand side, we have

`\begin{gathered} 100*\tan 86.1=h \\ or\text{ equivalently} \\ h=100*\tan 86.1 \end{gathered}`

therefore, the answer is

`h=1466.85\text{ ft}`

that is,by rounding up, the height is 1467 feets