how do i find the height of a triangle when all i am given is the angle of elevation and the length of the triangle I need help in figuring out how to find the height from a spotlight to the ceiling of some clouds if from a theodolite to the spotlight is 83m and the angle of elevation is 62.7°.

The measurement of altitude is vertical, so you have a right triangle with hypotenuse 83 and one angle 62.7 degrees. Look up the definitions of sine and cosine. Which should you apply?