Question

find the length of side $x$ to the nearest tenth.
triangle image with 30°, 60°, right angle, side 4, and side $x$

Explanation:

Step1: Identify trigonometric ratio

We use tangent, since we have the adjacent side to the 30° angle (length 4) and need the opposite side \(x\). The tangent formula is:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

Substitute $\theta = 30^\circ$, adjacent = 4, opposite = $x$:
$\tan(30^\circ) = \frac{x}{4}$

Step3: Solve for \(x\)

Rearrange to isolate \(x\) and calculate:
$x = 4 \times \tan(30^\circ)$
$\tan(30^\circ) = \frac{\sqrt{3}}{3} \approx 0.577$
$x \approx 4 \times 0.577 = 2.308$

Step4: Round to nearest tenth

Round 2.308 to one decimal place:
$x \approx 2.3$

Answer:

2.3