Question

In triangle ABC, how do you solve the right triangle given 12, 12 & 20 as sides?

Answer 1

Largest angle `~=1.970 ("radians") ~= 112.9^@`
Other two angles `~= 0.586 ("radians") ~= 33.6^@`

Explanation:

Note: despite the question statement, a triangle with sides `12, 12, 20` is not a right triangle (the sides do not satisfy the Pythagorean Theorem).

The Cosine Law tells us:
`cos(c) = (a^2+b^2-c^2)/(2ab)`

Setting `c` as the longest side (`20`)
we can calculate
`color(white)("XXX")cos(c) = 7/18`

Then use a calculator (or similar) determine
`color(white)("XXX")c= arcsin(7/18) = 1.970` (radians)

Similar calculations can be made for `a` and `b`
or
noting that `a=b` and `a+b+c=pi` we can calculate `a` and #b" that way.