Question

question 1 (multiple choice worth 1 points)
(05.01r lc)
a lamppost, cab, bent at point a after a storm. the tip of the lamppost touched the ground at point c, as shown below:
what is the height, in feet, of the portion ab of the lamppost?
\\(\frac{10}{\tan50^{\circ}}\\)
\\(\frac{10}{\cos50^{\circ}}\\)
10 \cos 50^{\circ}
10 \tan 50^{\circ}

Explanation:

Step1: Recall tangent formula

In right - triangle ABC, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 50^{\circ}$, the adjacent side to the angle $50^{\circ}$ is BC = 10 feet and the opposite side is AB.
$\tan50^{\circ}=\frac{AB}{BC}$

Step2: Solve for AB

Since BC = 10 feet, we can rewrite the equation as $AB = BC\times\tan50^{\circ}$. Substituting BC = 10, we get $AB = 10\tan50^{\circ}$.

Answer:

D. $10\tan50^{\circ}$