Precalculas chapter 8.1

Question

A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 800 ft out in the plain from the base of the mountain. Find the shortest length of cable needed. 

Answer 1

a right triangle is formed with 2 sides 3400 and 800, height = 3400, base = 800

the hypotenuse = sqr(3400^2 + 800^2) = about 3,492.84 feet = minimum cable distance

but check the tangent of 74 degrees = 3.487414444

it should equal 3400/800 = 34/8 = 4.25

there's an inconsistency or contradiction in the problem

you get different answers depending on which info you use