Angle Bisector Theorem?

Geometry Level 2

In a $\triangle ABC, AD$ is the bisector of the $\angle A.$ If $AB=3,AC=6$ and $BC=3\sqrt3,$ find the length of $AD.$
Give your answer to three decimal places.

The answer is 3.464.

1 solution

Ayush G Rai
May 26, 2016

Since $AB^2+BC^2=AC^2,\angle ABC=90^\circ.$
Now $sin\angle BAC=\frac{\sqrt3}{2}$
$\Rightarrow \angle BAC=60^\circ$
$\Rightarrow \angle BAD=30^\circ$
$\Rightarrow AD=3sec30^\circ=2\sqrt3\cong\boxed {3.464}.$

Angle Bisector Theorem?

The answer is 3.464.

1 solution

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