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

Question

(1 point)
Responses

45.22
45.22

96.68
96.68

88.19
88.19

81.12
81.12

Answer 1

To find the measure of segment AB, you can use the Law of Sines.

First, determine the measure of angle C:
m∠C = 180° - (m∠A + m∠B)
m∠C = 180° - (55° + 44°)
m∠C = 180° - 99°
m∠C = 81°

Use the Law of Sines formula:
a/sin A = b/sin B = c/sin C

Substitute the known values:
AB/sin 55° = 68/sin 44°

Now, solve for AB:
AB = 68 * sin 55° / sin 44°
AB ≈ 81.12

Therefore, the measure of segment AB is 81.12.