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

Step-by-step 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=(100)/(249) \\ inverse\text{ Tan in both sides} \\ \tan^(-1)(tan\theta)=\tan^(-1)((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