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 $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 60^{\circ}$, opposite side to $60^{\circ}$ is $A$ and adjacent side is $3$m.

Step2: Apply tangent formula

$\tan60^{\circ}=\frac{A}{3}$. Since $\tan60^{\circ}=\sqrt{3}$, we have $\sqrt{3}=\frac{A}{3}$.

Step3: Solve for A

Multiply both sides by 3: $A = 3\sqrt{3}\text{ m}$.

Answer:

$3\sqrt{3}\text{ m}$