Question

How do you solve for the unknown lengths and angle measures of triangle ABC where angle C = 90 degrees, a = 72 and angle A = 59?

Answer 1

`B= 90^circ-59^circ=31^circ`

`c = 72/sin 59^circ`

`b = 72/tan 59^circ`

Explanation:

Here we have a right triangle so there are shortcuts compared to the usual "solve this triangle."

The three angles add to `180^circ` so the remaining two in a right triangle add to `90^circ.` Those are called "complementary" and it's what the "co" in cosine refers to.

`B=90^circ - A = 90^circ-59^circ=31^circ`

`sin A = a/c`

`c = a/sin A = 72/sin 59^circ`

`tan A = a/b`

`b = a/ tan A = 72/tan 59^circ`

I don't like the calculator part and since it's not my homework I can leave it to you.