Question

the angle of elevation from the tip of a flagpoles shadow to the top of the flagpole is 58 degrees. the length of the shadow is 12 ft. find the height of the flagpole to the nearest tenth of a foot.

Answer 1

We will solve as follows:

*First: We will calculate the measurement of the hypotenuse formed by the top of the pole and the end of the shadow:

`12=h\cos (58)\Rightarrow h=(12)/(\cos (58))`
`\Rightarrow h=22.64495898\ldots\Rightarrow h\approx22.6`

*Second: We will now determine the height of the pole using the hypotenuse and the angle, that is:

`y=((12)/(\cos(58)))\sin (58)\Rightarrow y=19.20401435\ldots`
`\Rightarrow y\approx19.2`

From this, we have that the height of the pole is approximately 19.2 ft.