Question

Find $AB.$In Exercise $3,$$\overline{CB}$ is tangent to $\odot A.$

Short answer

The length of, $AB=15$.

Step-by-step solution

Step 1. Given information.

The given figure is as follows,

Step 2. Formula used.

$\tan \theta =\frac{\text{Opposite side}}{\text{Adjacent side}}$

Step 3. Put the data from the given figure.

$\begin{array}{l}\tan \theta =\frac{\text{Oppositeside}}{\text{Adjacentside}}\\ \tan 30°=\frac{AC}{AB}\\ \frac{1}{\sqrt{3}}=\frac{5\sqrt{3}}{AB}\\ AB=5\left(3\right)\\ =15\end{array}$

Therefore, the value of, $AB=15$.