Question

question
find the length of side ( x ) to the nearest tenth.
(right triangle with angles 30°, 60°, 90°, side ( sqrt{7} ) opposite 30°, side ( x ) opposite 60°)
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For the $30^\circ$ angle, opposite side is $\sqrt{7}$, adjacent is $x$.
$\tan(30^\circ)=\frac{\sqrt{7}}{x}$

Step2: Rearrange to solve for $x$

$x=\frac{\sqrt{7}}{\tan(30^\circ)}$
Since $\tan(30^\circ)=\frac{1}{\sqrt{3}}$, substitute:
$x=\sqrt{7} \times \sqrt{3}=\sqrt{21}$

Step3: Calculate decimal value

$\sqrt{21}\approx4.583$

Step4: Round to nearest tenth

Round 4.583 to one decimal place.

Answer:

$4.6$