Question

In △ABC, given (a=11), (b=20), and (c=28), find (m∠A) using the law of sines.

A. 15.3
B. 18.4
C. 28.0
D. 26.9

Answer 1

Using the Law of Sines, the measure of angle A (m∠A) in triangle ABC with sides a = 11, b = 20, and c = 28 is found to be approximately 15.3°. The answer is A. 15.3

Step-by-step explanation:

To find the measure of angle A (m∠A) in triangle ABC using the Law of Sines, we can set up a ratio involving the sides and angles of the triangle. Since we know the sides a = 11, b = 20, and c = 28, we can write:

ç = ç ç

Now we solve for sin A:

sin A = ç

The next step is to use the inverse sine function to find angle A. Be aware that we will only find an acute angle using this method, and if angle A is obtuse, some additional considerations may apply:

A = arcsin(ç)

By calculating the arcsin using a calculator, we get:

A ≈ 15.3° (Option A)

The answer is A, which indicates that m∠A is approximately 15.3 degrees.