Question

144 = 100 + 225 - 300cos(b)
find m∠b

Explanation:

Step1: Simplify the equation

$$144 = 100 + 225-300\cos(B)$$
$$144=325 - 300\cos(B)$$

Step2: Isolate the cosine term

$$300\cos(B)=325 - 144$$
$$300\cos(B)=181$$
$$\cos(B)=\frac{181}{300}$$

Step3: Find the angle

$$B=\cos^{-1}(\frac{181}{300})\approx52.9^{\circ}$$

Answer:

$m\angle B\approx52.9^{\circ}$