Question

If triangle ABC has the following measurements, find the measure of side c: a = 5 ,b = 7, C = 42°

A) 4.7
B) 5.8
C) 5.6
D) 5.2

Answer 1

The correct answer is A) 4.7.

Answer 2

Using the Law of Cosines, the measure of side c in triangle ABC is found to be approximately 4.7 units when a = 5, b = 7, and angle C is 42°.

Step-by-step explanation:

To find the measure of side c in triangle ABC, where side a is 5, side b is 7, and angle C is 42°, we can use the Law of Cosines. The Law of Cosines states: c² = a² + b² - 2ab cos(C). Substituting in the known values gives us:

c² = 5² + 7² - 2(5)(7) cos(42°)

c² = 25 + 49 - 70 cos(42°)

Using a calculator to find the cosine of 42° and then computing the expression, we get:

c² = 74 - 70(0.7431) ≈ 74 - 52.017

c² ≈ 21.983

Now take the square root of both sides:

c ≈ √21.983 ≈ 4.7

Therefore, the measure of side c is approximately 4.7 units, which corresponds to option A).