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?

1 Answer
Jun 4, 2018

#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.