For a triangle ABC, find the measure of AB given m∠A = 55°, m∠B = 44°, and b = 68

1 answer

To find the measure of AB, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:

a/sin A = b/sin B = c/sin C

Where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite each side, respectively.

We are given that m∠A = 55°, m∠B = 44°, and b = 68. We need to find a, the length of AB.

Using the law of sines, we have:

a/sin 55° = 68/sin 44°

Multiplying both sides by sin 55°, we get:

a = 68(sin 55°/sin 44°)

Using a calculator, we get:

a ≈ 85.6

Therefore, the measure of AB is approximately 85.6.