Question

calculate the value of the angle \\( \theta \\) in the following figure:

Explanation:

Step1: Convert units

Since \(1\ cm = 10\ mm\), then \(4\ cm=4\times10 = 40\ mm\).

Step2: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to \(\theta\) is \(40\ mm\) and the adjacent side is \(20\ mm\). So, \(\tan\theta=\frac{40}{20}\).

Step3: Calculate \(\theta\)

\(\tan\theta = 2\). Then \(\theta=\arctan(2)\). Using a calculator, \(\theta\approx63.43^{\circ}\).

Answer:

\(\theta\approx63.43^{\circ}\)