Question

the shadow of a building that is 28 m in height measures 20 m in length. draw a diagram and then determine the angle of the elevation of the sun.

Explanation:

Step1: Set up the right - triangle

We can consider a right - triangle where the height of the building is the opposite side ($a = 28$ m) and the length of the shadow is the adjacent side ($b = 20$ m) with respect to the angle of elevation of the sun $\theta$.

Step2: Use the tangent function

The tangent of an angle in a right - triangle is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan\theta=\frac{28}{20}=\frac{7}{5}=1.4$.

Step3: Find the angle

To find the angle $\theta$, we take the inverse tangent (arctan) of 1.4. So, $\theta=\arctan(1.4)$. Using a calculator, $\theta\approx54.46^{\circ}$.

Answer:

The angle of elevation of the sun is approximately $54.46^{\circ}$.