Question

In triangle ABC, AB=12, BC=18, and M < B=75. What are the approximate length of the side AC and measure of

A. AC = 20.3; m
B. AC = 18.9; m
C. AC = 20.3; m
D. AC = 18.9; m

Answer 1

The correct answer is option B. In triangle ABC with given side lengths and angle, we can find the length of side AC and measure of angle A using the Law of Cosines.

Step-by-step explanation:

In triangle ABC, we are given that AB = 12, BC = 18, and ∠B = 75°.

To find the length of side AC, we can use the Law of Cosines, which states that c² = a² + b² - 2ab cos C.

Using the given information, we can substitute the values into the equation: AC² = 12² + 18² - 2(12)(18)cos(75°).

By solving this equation using a calculator, we find that AC ≈ 18.9 units and the measure of angle A ≈ 39.1°.

Therefore, the approximate length of side AC is 18.9 units and the measure of angle A is 39.1°.