I have no idea how to find an angle when you have 2 sides of a right triangle

Question

It is a right triangle with two unknown angles and one unknown side length. The present lengths are 8 and 11. I need to find one of the angles. Please help!

Answer 1

Is 11 the Hypotenuse, or one of the sides?  If 11 is the hypotenuse, you can use the law of sines to help you...

 

Sin(A)/a = Sin(B)/b

 

Sin(90)/11 = Sin(B)/8

 

8/11=Sin(B)

 

B=46.6

 

The other angle would be 43.3

 

If 11 is not the hypotenuse, you can still use law of sines, you just have to use the Pythagorean Theorem first...

8^2+11^2=C^2

185=C^2

13.6=C

 

Then you could use the law of the sines with the new values.