Question

A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-foot-long shadow.100 ft249 ftThe angle of elevation to the nearest degree is2 3 456 78222435456668

Answer 1

the angle of elevation to the nearest degree is 22

Explanation

Step 1

set the equation:

we have a right triangle where

so

let

$\begin{gathered} angle\text{ =}\theta(unknown) \\ adjacent\text{ side=249 ft} \\ opposite\text{ side =100 ft} \end{gathered}$

hence, we need a function that relates those values, it is

$tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}$

therefore

Step 2

now, replaca and solve for angle

$\begin{gathered} tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}} \\ tan\theta=\frac{100}{249} \\ inverse\text{ Tan in both sides} \\ \tan^{-1}(tan\theta)=\tan^{-1}(\frac{100}{249}) \\ \theta=21.88° \\ rounded \\ \theta=22\text{ \degree} \end{gathered}$

therefore, the answer is

the angle of elevation to the nearest degree is 22

I hope this helps you