how do I find the height of a right angle triangle

What other information are you given?

 

If you have the length of the other two sides then you can use Pythagoras's theorem.

If you have an angle and one of the other sides then you can use a trigonometric function.

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GIVEN: Right Angle Triangle has the following characteristics - 90 degree angle & 2 sets of 45 degree composites (partners); therefore 90 + 45 + 45 = 180 degrees (THEOREM)

ie) sin (0) = height/hypotenuse;

let height = y-axis

let hypotenuse = z-axis (diagonal)

 

ie) sin (0) = y/z; therefore y(height) = z * (sin(0)), .. I think

THEN... sin (45 degrees) = blah blah blah