Question

unit exam - right triangles and trigonometry
solve for x.
10 in
x
20°
x = ? in
round to the nearest hundredth.
submit

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(20^\circ) = \frac{x}{10}$

Step3: Solve for x

$x = 10 \times \sin(20^\circ)$

Step4: Calculate and round

$\sin(20^\circ) \approx 0.3420$, so $x \approx 10 \times 0.3420 = 3.42$

Answer:

$3.42$ in