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:Triangle ABC has measure of angle C equal to 45 degrees, measure of angle ABC equal to 90 degrees, and length of BC equal to 12 feet.What is the height, in feet, of the portion AB of the lamppost? 12 tan 45° 12 divided by tan 45 degrees 12 divided by cos 45 degrees 12 cos 45°

Answer 1

Explanation

We are to obtain the value of the portion AB in the given triangle

Let the length of side AB be x

so that

Using the trigonometric ratio

$tan45^0=\frac{x}{12}$

Making x the subject of the formula

$\begin{gathered} x=12tan45^0 \\ x=12tan45^0\text{ } \end{gathered}$

Since AB=x

Therefore, the height of AB is

$AB=12\text{ tan 45}^0$