Question

what is x to the nearest tenth?

a

31

22

c

39

b

a. 37.5

b. 52.5

c. 75.0

d. 103.0

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In \(\triangle ABC\), let \(a = 31\), \(b = 39\), \(c = 22\), and \(C=x\). Then \(22^{2}=31^{2}+39^{2}-2\times31\times39\times\cos x\).

$$484 = 961+1521-2418\cos x$$

$$484=2482 - 2418\cos x$$

$$2418\cos x=2482 - 484$$

$$2418\cos x = 1998$$

\(\cos x=\frac{1998}{2418}\approx0.826\)

Step2: Find the angle \(x\)

\(x=\cos^{-1}(0.826)\)
Using a calculator, \(x\approx37.5^{\circ}\)

Answer:

A. \(37.5\)