Question

find the length of side x to the nearest tenth.
(right triangle with angles 30°, 60°, right angle, side adjacent to 30° is 4, hypotenuse is x)
answer attempt 1 out of 2
x = submit answer

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
For the $30^\circ$ angle, opposite side is $4$, hypotenuse is $x$.

Step2: Set up the equation

$\sin(30^\circ)=\frac{4}{x}$

Step3: Solve for $x$

Rearrange to $x=\frac{4}{\sin(30^\circ)}$. Since $\sin(30^\circ)=0.5$,
$x=\frac{4}{0.5}=8.0$

Answer:

$8.0$