Question

find the length of side ( x ) in simplest radical form with a rational denominator.
right triangle with angles 30°, 60°, 90°, one leg 4, hypotenuse ( x )
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify trigonometric ratio

We use the tangent function, where $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For the $60^\circ$ angle, opposite side is $x$, adjacent side is 4.
$\tan(60^\circ)=\frac{x}{4}$

Step2: Substitute $\tan(60^\circ)$ value

We know $\tan(60^\circ)=\sqrt{3}$, so substitute this into the equation.
$\sqrt{3}=\frac{x}{4}$

Step3: Solve for $x$

Multiply both sides by 4 to isolate $x$.
$x=4\sqrt{3}$

Answer:

$x=4\sqrt{3}$