Question

the equation $sec(25^{circ})=\frac{9}{c}$ can be used to find the length of $overline{ab}$. what is the length of $overline{ab}$? round to the nearest tenth. 19.3 in 21.3 in 23.5 in 68.0 in

Explanation:

Step1: Recall tangent formula in right - triangle

In right - triangle $ABC$ with $\angle A = 25^{\circ}$ and $BC = 9$ in, $\tan(A)=\frac{BC}{AC}$. Given $\tan(25^{\circ})=\frac{9}{AC}$.

Step2: Solve for $AC$

We can rewrite the equation as $AC=\frac{9}{\tan(25^{\circ})}$. Since $\tan(25^{\circ})\approx0.4663$, then $AC=\frac{9}{0.4663}\approx19.3$.

Answer:

19.3 in