Can I find the length of an right angle triangle, from one side and two angles?

Question

In my c++ application I have a 3d plane, with a point above it. The plane is rotated, and the point is at 0,0,0.

In the image below, the plane is represented by the triangle side B - C. (S3)

A is the point that is at zero. B is the mid-point of the plane.

What I need to calculate is the distance from Point A, to where it intersects the plane (Point C).

I know the angle of the plane, and the coordinates of point A and Point B.

Point A is at (xyz) 0,0,0; Point B is at: -1,2.7,-19.7;

From this, i know the length of Side S2 (19.7). The angle of Angle B is 17.675 degrees.

So I now have one side and one angle. I know that the corner at point C is 90 degrees. Is this enough to get me the length of the the side S1?

Answer 1

Yes we can, indeed recall that

• $S_3=S_2 \cos B$
• $S_1=S_2 \sin B$

Answer 2

Yes, the right triangle is uniquely determined by its hypotenuse and an angle $\alpha.$

The other two sides are $$ BC=AB cos( \alpha) \\AC= AB sin( \alpha)$$