Question

A ski slope has an incline of 64 (its angle of elevation is 64). The slope has an elevation of 3873 feet. At the bottom of the slope is a flat (horizontal) run out, and 898 feet from the slope is the end of a cable (the other end is at the top of the slope.) How long is the cable?

Answer 1

as we compute sin 64= 0.899 and cos 64=0.438
consider triangle ABC ,AB =AC*sin 64=3873*0.899=3481.27
and BC=AC*cos 64=3873*0.438=1696.374
DB=DC+CB=898+1696.374
so tan D=AB/DB=3481.27/2594.374=1.314
so D=52.728 degrees( using calculator)
so AB=AD*sin52.728 or AD=AB/sin 52.728
AD= 4374.72 m is the cable length