Question

in the right triangle, one leg is 11, the acute angle is 30°, and the other leg (adjacent to 30°) is x. find the value of x.

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta=30^\circ$, opposite side $=11$, adjacent side $=x$.

Step2: Substitute values into formula

$\tan(30^\circ) = \frac{11}{x}$
We know $\tan(30^\circ)=\frac{1}{\sqrt{3}}$, so:
$\frac{1}{\sqrt{3}} = \frac{11}{x}$

Step3: Solve for x

Cross-multiply to isolate $x$:
$x = 11\sqrt{3}$
We can also write this as a decimal approximation: $x\approx11\times1.732=19.052$

Answer:

$x=11\sqrt{3}$ or approximately $19.05$