A new volcano has suddenly appeared where a small strip mall used to be. You are the head of the intrepid surveying crew whose job it is to determine the height of the peak. Traveling bravely toward the volcano, you stop at a safe distance and measure an angle of elevation of 21� to the top. You continue resolutely for another half mile and measure an angle of elevation of 35�. You and your crew had better not get any closer just now — there’s a new spew of ash coming out from the peak. So retreat, do some calculating, and tell the waiting reporters just how tall the volcano is. (They’ll want the answer in feet, of course.)

Show/Hide Solution

We fill in all the angles.
We’ll get VS by using the Law of Sines, then h from △VSB.

2640  =  VS  → VS =  2640 sin 21  ≈3905
sin 14 sin 21 sin 14

h  = sin 35 → h = 3905 sin 35 ≈ 2241 feet, or about .4 of a mile.

That’s a mighty big eruption to happen suddenly!

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