Use trig ratios to solve for x

Feb 2018
29
1
California
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!

Screen Shot 2020-03-04 at 12.54.42 PM.png
 
Feb 2010
738
162
What is the sum of the three angles of a triangle? Use the law of sines.
 
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Feb 2018
29
1
California
Actually, I figured it out! Thanks anyway.
 

skipjack

Forum Staff
Dec 2006
21,481
2,470
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 $x$.
 
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