# Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. How do you find the slope?

Jun 4, 2018

$\sqrt{{1800}^{2} + {17160}^{2}} = c$ therefore the slope, should be: 17254.15ft

#### Explanation:

Lovely question, we're dealing with pythagoras. this is where you always want to draw a diagram

so, you're ascending 1800ft and moving 3.25 miles across
now let's convert miles to feet firstly. so 3.25mi it about 17160ft
now, you can convert any value into any other, you may want your triangle in ft, m, whatever, I'm doing feet here as it seems to be the nicest one to work in.

Next up remember 1800ft is the verticle axis and 17160ft is the horizontal

Pythagorean theorem states ${a}^{2} + {b}^{2} = {c}^{2}$ where a and b are the two sides you know, for this case we'll take a as 1800ft and b as 17160ft

so.. ${1800}^{2} + {17160}^{2} = {c}^{2}$ therefore $\sqrt{{1800}^{2} + {17160}^{2}} = c$ therefore the slope, should be: 17254.15ft