Thread: Triangle Problem

You may use any pre-calculus/trigonometric procedure to solve the problem. In any case please explain everything.

the lengths of the sides of a triangle are 25, 29, 36. there is a
point on the longest side of the triangle whose distance from the
opposite vertex is 20. what is the distance from this point to the
midpoint of the shortest side?

IF there are multiple answers please describe all of them.
IF there are no answers please explain why.

Thank you!

Originally Posted by Skyrim

You may use any pre-calculus/trigonometric procedure to solve the problem. In any case please explain everything.

the lengths of the sides of a triangle are 25, 29, 36. there is a
point on the longest side of the triangle whose distance from the
opposite vertex is 20. what is the distance from this point to the
midpoint of the shortest side?

IF there are multiple answers please describe all of them.
IF there are no answers please explain why.

Thank you!

I would start with the triangle on a coordinate grid to make things easier.

Your first task is to solve for x.

Once you find x, you can then use coordinate geometry to find solutions to your problem.

Label triangle ABC: AC=25, AB=29, BC=36 ; make D the point on BC distance 20 from A
Calculate angle at C
Triangle ACD: you have AC=25, AD=20 and angle C; results in ACD = right triangle
Continue...

Smallesrt side AB = 25.

Largest side BC = 36.

D ia a point on BC such that AD = 20.

Now ADB is a right angled triangle.

If E is the mid point of AB, then DE = AE = BE.

Then what is DE?