Question

find the length of side ( x ) to the nearest tenth.
(there is a right triangle with one angle ( 30^circ ), one angle ( 60^circ ), the hypotenuse is 5, and the side opposite to ( 60^circ ) is ( x ))

Explanation:

Step1: Identify trigonometric ratio

For the 30° angle, side $x$ is adjacent, and the hypotenuse is 5. Use cosine:
$\cos(30^\circ) = \frac{x}{5}$

Step2: Solve for $x$

Rearrange to isolate $x$:
$x = 5 \times \cos(30^\circ)$
Substitute $\cos(30^\circ) = \frac{\sqrt{3}}{2}$:
$x = 5 \times \frac{\sqrt{3}}{2}$

Step3: Calculate and round

Compute the value:
$x = \frac{5\sqrt{3}}{2} \approx 4.330$
Round to the nearest tenth:
$x \approx 4.3$

Answer:

4.3