Question

by first finding tan θ, calculate the size of angle θ. give your answer to the nearest degree. not drawn accurately 6 cm 13 cm

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to angle $\theta$ is $6$ cm and the adjacent side is $13$ cm. So, $\tan\theta=\frac{6}{13}$.

Step2: Calculate the angle

We know that $\theta = \arctan(\frac{6}{13})$. Using a calculator, $\theta=\arctan(\frac{6}{13})\approx 24.78^{\circ}$. Rounding to the nearest degree, $\theta\approx25^{\circ}$.

Answer:

$25^{\circ}$