Question

the equation sin(25°) = 1/2 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. 23.5 in. 21.3 in. 68.0 in.

Explanation:

Step1: Recall sine - definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin(25^{\circ})=\frac{10}{c}$, where $c$ is the length of $\overline{AB}$ and assume the opposite side to the $25^{\circ}$ angle has length 10 (not shown in the problem statement but we need some value for the opposite side to solve, and we can work backward from the sine formula). So $c=\frac{10}{\sin(25^{\circ})}$.

Step2: Calculate the value of $c$

We know that $\sin(25^{\circ})\approx0.4226$. Then $c = \frac{10}{0.4226}\approx23.66$. Rounding to the nearest tenth, $c\approx23.5$.

Answer:

23.5 in