Question

A ladder 35.4 feet long is leaning against an embarkment inclined 62.5 degrees to the horizontal. If the bottom of the ladder is 10.2 feet from the embarkment, what is the distance from the top of the ladder down the embarkment to the ground?

Answer 1

If the ladder makes an angle A with the ground and B with the embankment, then using the law of sines,

35.4/sin 117.5 = 10.2/sinB = x/sinA

Now you can find B, and A = 180-(117.5+B) and you can find x.

Answer 2

or, having found B, you can use the law of cosines:

x^2 = 35.4^2 + 10.2^2 - 2(35.4)(10.2)cosB