find the angle of elevation from point c to point a. angle of elevation = ?°

Explanation:

Step1: Recall tangent - ratio formula

In right - triangle ABC, $\tan\theta=\frac{opposite}{adjacent}$, where $\theta$ is the angle of elevation from C to A, the opposite side to the angle of elevation is AB and the adjacent side is BC. First, we need to find the length of BC. In right - triangle ABC, $\tan59^{\circ}=\frac{BC}{AB}$. Given $AB = 402$ m, then $BC=AB\tan59^{\circ}=402\times\tan59^{\circ}$.

Step2: Calculate the angle of elevation

Let the angle of elevation from C to A be $\alpha$. Then $\tan\alpha=\frac{AB}{BC}$. Since $BC = 402\times\tan59^{\circ}$ and $AB = 402$, $\tan\alpha=\frac{402}{402\times\tan59^{\circ}}=\cot59^{\circ}=\tan(90 - 59)^{\circ}=\tan31^{\circ}$. So, $\alpha = 31^{\circ}$.

Answer:

$31$