In △abc, m∠cab = 60° and ad is angle bisector with d∈ bc and ad=8ft. find the distances from d to the sides of the triangle.

The distances from D to the both sides(AB and AC) of the triangle are 4 ft.

Explanation

In the diagram below, ABC is a triangle in which ∠CAB = 60°

As,  AD is the angle bisector of ∠CAB, that means ∠CAD = ∠DAB = 30°

The distance from D to side AC is  DE and distance from D to side AB is  DF. That means both ∠AED and ∠AFD are right angle.

Given that, the length of AD = 8 ft.

So, in right angle triangle AED.....

Also, in right angle triangle AFD....

So, the distances from D to the both sides(AB and AC) of the triangle are 4 ft.

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