Question

find the measure of the indicated angle. 11 \boxed{?}^\circ 12 20

Explanation:

Step1: Apply Law of Cosines

We use the Law of Cosines formula for the unknown angle $\theta$ opposite the side of length 12:
$$\cos\theta = \frac{a^2 + c^2 - b^2}{2ac}$$
Here, $a=11$, $c=20$, $b=12$.

Step2: Substitute values into formula

$$\cos\theta = \frac{11^2 + 20^2 - 12^2}{2 \times 11 \times 20}$$
$$\cos\theta = \frac{121 + 400 - 144}{440}$$
$$\cos\theta = \frac{377}{440} \approx 0.8568$$

Step3: Calculate inverse cosine

$$\theta = \cos^{-1}(0.8568) \approx 31^\circ$$

Answer:

$31^\circ$