Estimation of distance.

Question

6. A volcano is about to erupt and the volcanologist on site needs to know the distance from his position at the base of the mountain to the summit. The only data he has is the elevation of the summit in feet above sea level (4,735 ft) and the diameter across the base of the volcano (6.4 miles). What is an estimation of the distance from the volcanologist to the summit?

Answer 1

Assuming the shape of the volcano is roughly a cone, we're dealing with a right triangle problem. The vertical leg of the triangle would be the elevation of the volcano: 4735ft. The horizontal leg would be the radius of the base: 6.4mi./2 = 3.2mi. = 16896ft.

 

Thus, we can apply Pythagoras' theorem to find the distance required:

 

dist² = (4735)² + (16896)²

dist² = 22420225 + 285474816

dist² = 307895041

dist = 17546.9ft., approximately

 

...or about 3.323 miles.