Yesterday I learned to solve a right triangle assuming I know the 3 angles and 1 side. I can now establish the lengths of the 2 other sides using a sine table I printed off the net.

Today I hope I will learn to solve a right triangle but now I only know 1 angle (the right angle) and 2 sides (not the hypotenuse). How do I establish the other 2 angles?

Help please.

Thank you,

Mike.

You know two sides, a and b. Compute the third side length with c^2 = a^2 + b^2. Then use
a/c = sin A
b/c = sin B = cos A
to solve for the two angles. You can use either a sine table or an arcsine table.

To solve a right triangle when you know one angle (which is the right angle) and two sides (not the hypotenuse), you can follow these steps:

1. Start by labeling the right angle as 90 degrees.
2. Label the two sides you know as 'a' and 'b'.
3. Use the Pythagorean theorem to find the length of the third side, which is the hypotenuse 'c'. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides: c^2 = a^2 + b^2.
For example, if 'a' is 3 and 'b' is 4, then you would have: c^2 = 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of both sides, you get: c = 5.
So the length of the third side (the hypotenuse) is 5.

4. Once you have found the length of the hypotenuse, you can use trigonometric ratios to find the two other angles.
- To find angle A, use the ratio of the length of side 'a' to the length of the hypotenuse 'c'. You can use the sine function: sin A = a / c.
For example, using the previous values, sin A = 3 / 5 = 0.6. To find the actual angle, you can use a sine table or an arcsine (inverse sine) function. If you use an arcsine table, you would find that arcsin 0.6 is approximately 36.87 degrees. So angle A is approximately 36.87 degrees.

- To find angle B, use the ratio of the length of side 'b' to the length of the hypotenuse 'c'. In a right triangle, angle B is the complement of angle A, so it can also be found using the cosine function: cos B = a / c.
Using the previous values again, cos B = 4 / 5 = 0.8. Similarly, you can use a cosine table or an arccosine (inverse cosine) function to find the angle. Arccos 0.8 is approximately 36.87 degrees as well. So angle B is also approximately 36.87 degrees.

Therefore, in this example, both angle A and angle B would be approximately 36.87 degrees.

Remember to adjust the process based on the values of 'a' and 'b' that you have.