In triangle ABC, measure angle A equals 37 degrees, measure angle B equals 63 degrees and BC equals 14 inches What is AB to the nearest tenth?

Answer 1

To find the length of side AB, we can use the Law of Sines.

First, we need to find the measure of angle C. Since the sum of the angles in a triangle is 180 degrees, we have:

A + B + C = 180 degrees
37 + 63 + C = 180
100 + C = 180
C = 180 - 100
C = 80 degrees

Now we can use the Law of Sines:

sin A / BC = sin B / AC = sin C / AB

sin 37 / 14 = sin 63 / AC = sin 80 / AB

We can solve for AC first:
sin 63 = AC / 14
AC = 14 * sin 63
AC ≈ 12.6 inches

Now we can solve for AB:
sin 80 = AB / 12.6
AB = 12.6 * sin 80
AB ≈ 12.3 inches

Therefore, AB is approximately 12.3 inches to the nearest tenth.