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?
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.