# Chapter 11 - Section 11.2 - The Cosine Ratio and Applications - Exercises: 28

$\alpha=53.1$ $\beta=36.9$ $\phi=53.1$ $\theta=36.9$

#### Work Step by Step

$6^{2}+8^{2}=DB^{2}$ $36+64=DB^{2}$ $DB^{2}=100$ $DB=10$ $\cos\alpha=\frac{6}{10}$ $\alpha=\cos^{-1}\frac{6}{10}$ $\alpha=53.1$ $\cos\theta=\frac{8}{10}$ $\theta=\cos^{-1}\frac{8}{10}$ $\theta=36.9$ Because $\overline{AD}$ is parallel to $\overline{BC}$, this means $\theta = \beta$ and $\alpha=\phi$ as they are alternating angles. $\alpha=\phi=53.1$ $\theta=\beta=36.9$

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