Find the measure of θ . Round your answer to the nearest whole number. No hypotenuse, Adjacent = 5cm, Opposite = 2 cm

Answer 1

To find the angle $\theta$ in a right triangle where you know the lengths of the opposite side and the adjacent side, you can use the tangent function:

$$\tan (\theta )=\frac{\text{Opposite}}{\text{Adjacent}}$$

In this case, the opposite side is 2 cm and the adjacent side is 5 cm:

$$\tan (\theta )=\frac{2}{5}$$

Next, you will use the arctangent function (also known as the inverse tangent) to find $\theta$:

$$\theta ={\tan }^{-1}\left(\frac{2}{5}\right)$$

Using a calculator:

$$\theta \approx {21.80}^{\circ }$$

Rounding to the nearest whole number:

$$\theta \approx {22}^{\circ }$$

Therefore, the measure of $\theta$ is approximately ${22}^{\circ }$.