Question

find the length of side x to the nearest tenth.
(there is a right triangle with a right angle, one angle is 60°, one angle is 30°, the side adjacent to 30° and the right angle is 8, the side adjacent to 60° and the right angle is x)
answer attempt 1 out of 2
x =
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Explanation:

Step1: Identify trigonometric ratio

For the 60° angle, side $x$ is adjacent, side 8 is opposite. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(60^\circ)=\frac{8}{x}$

Step2: Rearrange to solve for $x$

Isolate $x$ by cross-multiplying.
$x=\frac{8}{\tan(60^\circ)}$

Step3: Calculate the value

Substitute $\tan(60^\circ)=\sqrt{3}\approx1.732$
$x=\frac{8}{1.732}\approx4.6$

Answer:

$4.6$