Question

applying a trigonometric ratio to find a side length
find the value of c, rounded to the nearest hundredth.

• when using trigonometric values, set your calculator to degrees.
• you can find the keys for trigonometric functions in the alternate keys.

\\(\sin(a)=\frac{opposite}{hypotenuse}\\)
\\(\sin(58^\circ)=\frac{4.25}{c}\\)
\\(c \cdot \sin(\underline{\quad\quad}^\circ)=\frac{4.25}{c} \cdot c\\)
\\(c=\frac{4.25}{\sin(58^\circ)}
= 5.011508
\approx 5.01\\)

Explanation:

Step1: Recall Sine Ratio

In a right triangle, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle A = 58^\circ$, opposite side is $4.25$, hypotenuse is $c$. So $\sin(58^\circ)=\frac{4.25}{c}$.

Step2: Solve for \( c \)

Rearrange the formula: $c=\frac{4.25}{\sin(58^\circ)}$. Calculate $\sin(58^\circ)\approx0.8480$. Then $c=\frac{4.25}{0.8480}\approx5.01$.

Answer:

\( c \approx 5.01 \)