If I have one side of a triangle and know the adjacent angles, is there a formula for determining the lengths of the other two sides?

Question

Side A is 35.5 in. And the adjacent angles are 15 and 90 degrees respectively. 

Answer 1

Yes,

 

The third angle must 75, because the angles inside the triangle must add up to 180.

 

Since this is a right triangle, you can use trig functions.

The side whose adjacent angles are 90 and 75 can be found using the tangent function.

Specifically, tan 75 = 35.5/?

 

               tan 75 = 3.73205080757...  found using calculator or table lookup

 

             Solving for the missing side ,  ? = 35.5 / tan75 = 35.5/3.763205080757.... = 9.5121963313048561....

 

Finally, the hypotnuse is found using the pythagorean theorem:

 

   square root of ( 9.5121963313048561 ^2 + 35.5 ^2)

 

          36.75, approximately