Question

In △ABC,a=14 , b=17 , and c=22 . Find m∠A . law of sines 4 A. 49.4 B. 39.5 C. 55.2 D. 50.45

Answer 1

To find the measure of angle A in triangle ABC, we can use the Law of Sines. The answer is B. 39.5 degrees.

Step-by-step explanation:

To find the measure of angle A in triangle ABC, we can use the Law of Sines. The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C). In this case, we know that a = 14, b = 17, and c = 22. Let's solve for angle A:

a/sin(A) = c/sin(C)

14/sin(A) = 22/sin(C)

Cross-multiply:

22sin(A) = 14sin(C)

Divide both sides by 22:

sin(A) = (14/22)sin(C)

Since sin(C) is between 0 and 1, we can conclude that sin(A) is also between 0 and 1. Therefore, angle A is less than 90 degrees. Looking at the answer choices, the only option that is less than 90 degrees is option B which is 39.5 degrees. So, the answer is B. 39.5 degrees.