Question

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?
20
20 tan 55°
20 cos 55°
20/tan 55°
20 cot 55°

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 55^{\circ}\), the adjacent side to the \(55^{\circ}\) angle is \(20\) (length \(BC\)), and the opposite side is \(AB\) (the height we want to find).

Step2: Set up the tangent formula

Let \(AB = h\). Then \(\tan55^{\circ}=\frac{h}{20}\).

Step3: Solve for \(h\)

Multiply both sides of the equation \(\tan55^{\circ}=\frac{h}{20}\) by \(20\). We get \(h = 20\tan55^{\circ}\).

Answer:

\(20\tan55^{\circ}\)