Question

find the value of variable x. if your answer is not an integer, write it in simplest radical form with the denominator rationalized.
(simplify your answer. type an integer or a simplified fraction.)
x = \square

Explanation:

Step1: Identify triangle sides/angles

This is a 30-60-90 right triangle. Hypotenuse = 10, $x$ is adjacent to $60^\circ$ angle.

Step2: Use cosine definition

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(60^\circ) = \frac{x}{10}$

Step3: Substitute $\cos(60^\circ)$ value

$\cos(60^\circ) = \frac{1}{2}$, so $\frac{1}{2} = \frac{x}{10}$

Step4: Solve for $x$

$x = 10 \times \frac{1}{2}$

Answer:

5