Question

In △ABC, m∠CAB = 60°, AD is the angle bisector of ∠BAC with D ∈ BC
and AD = 8ft. Find the distances from point D to the sides of the triangle.

pls don't use trigonometry

Answer 1

Answer: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.