# The figure shows △ABC.¯¯BD¯ is the angle bisector of ∠ABC. What is AD ?

Jan 10, 2017

2.67

#### Explanation:

In triangle ABC Tan B= $\frac{6}{8}$
Therefore angle B = $36.87 \mathrm{de} g r e e s$

So angle ABD =$\frac{36.87}{2} = 18.43 \mathrm{de} g r e e s$

Looking at triangle ABD
Tan 18.43=$\frac{A D}{8}$

Jan 10, 2017

$A D = 2.67$

#### Explanation:

As $A D$ is bisector of $\angle A$ from angle bisector theorem, we have

$\frac{A D}{D C} = \frac{A B}{B C} = \frac{8}{10} = \frac{4}{5}$

Hence we should divide $A C$ in the ratio $4 : 5$

and hence $A D = \frac{4}{4 + 5} \times 6 = \frac{24}{9} = \frac{8}{3} = 2.67$