Question

1. find the measure of the indicated angle, to the nearest degree.4

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula for finding an angle $\theta$ in a triangle with sides $a$, $b$, $c$ is $\cos\theta=\frac{a^{2}+b^{2}-c^{2}}{2ab}$. Let $a = 18$, $b=24$, $c = 21$. We want to find $\angle H$. So, $\cos H=\frac{18^{2}+24^{2}-21^{2}}{2\times18\times24}$.

Step2: Calculate the numerator

$18^{2}=324$, $24^{2}=576$, $21^{2}=441$. Then $18^{2}+24^{2}-21^{2}=324 + 576-441=459$.

Step3: Calculate the denominator

$2\times18\times24=864$.

Step4: Find the cosine value

$\cos H=\frac{459}{864}\approx0.5313$.

Step5: Find the angle

$H=\cos^{-1}(0.5313)$. Using a calculator, $H\approx58^{\circ}$.

Answer:

$58^{\circ}$