Question

A flagpole is located at the edge of a sheer y = 40-ft cliff at the bank of a river of width x = 30 ft. See the figure below. An observer on the opposite side of the river measures an angle of 9° between her line of sight to the top of the flagpole and her line of sight to the top of the cliff. Find the height of the flagpole. (Round your answer to one decimal place.)

Answer 1

There is no figure below because I can't copy and paste the photo

Answer 2

Use attachment

Answer 3

The angle just below is 53.13 as angle=arc tan (40/30) gives you the angle
Now see the whole right triangle including the flagpole so tan (53.13+9)=(y+h)/x gives you h=16.73

Answer 4

below 9 is 53.13

Answer 5

Ask me if there is any problem with the explanation

Answer 6

flag length is:\[30 \text{Tan}\left[\text{ArcTan}\left[\frac{40}{30}\right]+\frac{\pi }{20}\right]-40=16.7 \text{ feet} \]

Answer 7

Solution equation is:\[\frac{f+40}{30}=\text{Tan}\left[\text{ArcTan}\left[\frac{40}{30}\right]+\frac{\pi }{20}\right] \]