Question

In triangle abc mesure of angle cab is 60, ad is the angle bisector of angle bac with d intersecting bc and ad=8 find the distence from point d to the side of the triangle

a) 8√3 units
b) 8 units
c) 4√3 units
d) 4 units

Answer 1

In triangle ABC, with angle CAB measuring 60 degrees and AD as the angle bisector of angle BAC, intersecting BC and AD measuring 8, the distance from point D to the side of the triangle is 4 units.

Step-by-step explanation:

In triangle ABC, the measure of angle CAB is 60 degrees. AD is the angle bisector of angle BAC, intersecting BC, and AD = 8. We need to find the distance from point D to the side of the triangle.

Since AD is the angle bisector of angle BAC, we can use the Angle Bisector Theorem to find the length of BD and DC. Let x be the length of BD and y be the length of DC. According to the Angle Bisector Theorem, BD/DC = BA/CA = c/b, where c and b are the lengths of the sides opposite to angles CAB and BAC respectively. In triangle ABC, c = 8 and b = 8 + x + y. Substitute the values into the equation: x/y = 7/8.

The length of BD and DC can be found using the equation x + y = 8. Substitute x = (7/15) * 8 into the equation to find the value of y. Then, substitute the value of y into the equation x + y = 8 to find the value of x. The distance from point D to the side of the triangle is the length of BD or DC.

After solving the equations, we find that x = 4 and y = 4. So, the distance from point D to the side of the triangle is 4 units. Therefore, the correct answer is option (d) 4 units.