Question

find the missing side.
19
36°
x
x = ?

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle with hypotenuse \( 19 \) and we need to find the side opposite the \( 36^\circ \) angle. The sine function relates the opposite side and the hypotenuse: \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \).

Step2: Substitute the values

Here, \( \theta = 36^\circ \), hypotenuse \( = 19 \), and opposite side \( = x \). So, \( \sin(36^\circ)=\frac{x}{19} \).

Step3: Solve for \( x \)

Multiply both sides by \( 19 \): \( x = 19\times\sin(36^\circ) \). Calculate \( \sin(36^\circ)\approx0.5878 \), then \( x\approx19\times0.5878 \approx 11.17 \).

Answer:

\( x\approx11.17 \) (or more precise value depending on calculator precision, e.g., using more decimal places for \( \sin(36^\circ) \))