A mountain is inclined 80 degree s to the horizontal and has

A mountain is inclined 80 degree s to the horizontal and has a height of 1900 ft. A tram is to be installed 250 feet from the base, and run to the top of the mountain I km cable is needed? (this is the side labeled x) You may use a calculator.

Solution

Right angled triangle with 80 deg:

tan 80 = 1900/y

y = 1900/tan80 = 335 ft

So, Apply pythgoras theorem to larger triangle :

x^2 = (250+335)^2 + 1900^2

= 1988 ft cable length