Math question

Question

A 25ft water slide has a 10.8ft ladder which meets the slide at a 100 degree angle. To the nearest tenth, what is the distance between the end of the slide and the bottom of the ladder? 

Answer 1

usually the number of degrees for ladders is < 90, but I'll go with the 100.

 

I made a sketch of a triangle; side x is the 'base' (dist. between end of slide & ladder's foot).

the ladder makes an 80 degree angle INSIDE this triangle, and its length is labeled 10.8 ft.

the third side is labeled 25 ft.

 

Using the Law of Cosines: 25² = x² + 10.2² - 2(x)(10.8)cos 80^o

SOLVE THIS EQUATION for x.