# Use trig ratios to solve for x

#### mjsilverfly

Hi....I can get partially through this, but not sure how to finish to find x. I would drop a perpendicular from the top to create two right triangles. Then I could find the longer side of x (the left-hand triangle....I got 10.2 for that). Then I am left with the right triangle on the right side, which has angles 33 degrees, 90 degrees, and 57 degrees. But then what? I am stuck! How can I find the rest of that side? Please show step by step so I can understand. Thank you!

#### mrtwhs

What is the sum of the three angles of a triangle? Use the law of sines.

topsquark

#### mjsilverfly

Actually, I figured it out! Thanks anyway.

#### skipjack

Forum Staff
From the given angles, the third angle has to be 80$^\circ$, but the diagram makes it look like an obtuse angle. If one ignores that, $x/\sin(80^\circ)= 14/\sin(57^\circ)$, which allows you to calculate $x$.

topsquark