A triangle with the hypotenuse measuring 8, and the short leg measuring 5, and the the long leg measuring 7. How do you find the angles C the top angle, B the lower right angle, A the left angle?
Ignoring the (false) implication that we are dealing with a right angled triangle, we can use the Law of Cosines to determine the 3 angles
I have assumed that the triangle looks like:
The reference to a hypotenuse implies a right-angled triangle but based on the Pythagorean Theorem this is clearly false.
The Law of Cosines for a triangle with sides
which can be re-arranged as:
and similarly for angles
Plugging in the values for