Question

Explain to a new geometry student how to calculate m 14 years ago

Answer 1

Taking the sin/cos/tan of an angle gives you a ratio. This process can be reversed with arcsin, arccos, and arctan. Just like you hit the sin button on your calculator to find the sin of an angle, you hit the arcsin button to find the angle of a ratio. Arctan and tan are inverse functions, so they're exact opposites. Because of this, arctan is sometimes written as tan^-1. Inverse means they undo each other.

tan A = 1.2
Arctan of both sides.
arctan tan A = arctan 1.2
m<A = arctan 1.2
m<A approx = 50.19 degrees