The cable supporting a ski lift rises 2 feet for each 5 feet of horizontal length. The top of the cable is fastened 1320 feet above the cable’s lowest point. Find the lengths b and c, and find the measure of the angle theta.
The resulting triangle is a right triangle with the third side given: First, the angle can be solved using the given rise and run of the cable. So, tan θ = 2 / 5 θ = 15.95°
Next, the lengths b and c can be solved using the solved angle: tan 15.95 = 1320 / b b = 3300 ft
The hypotenuse or c can be solved by trigonometric functions or using Pythagorean theorem, using the sine function: sin 15.95 = 1320 / c c = 4804 ft
