Question

use your calculator and your knowledge of trigonometry to calculate side a in this right angled triangle.

Explanation:

Step1: Identify trigonometric ratio

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, if we consider the $60^{\circ}$ angle, the opposite side is $A$ and the adjacent side is $3$m.
$\tan60^{\circ}=\frac{A}{3}$

Step2: Recall value of $\tan60^{\circ}$

The value of $\tan60^{\circ}=\sqrt{3}$. So, $\sqrt{3}=\frac{A}{3}$.

Step3: Solve for $A$

Multiply both sides of the equation by $3$: $A = 3\sqrt{3}\text{m}\approx3\times1.732 = 5.196\text{m}$

Answer:

$3\sqrt{3}\text{m}\approx5.2\text{m}$