Length of Line from 90° Angle in 3-4-5 Triangle

[kenewbie]

In a 3-4-5 triangle, how long is a line extending from the 90 degree angle down to the middle of the hypothenus.

Thats all I've been given. I think I am supposed to figure this out without trig, just basic geometric properties. But I'm stumped.

I can see that the hypothenus is divided into two 2.5 halves, but I can't seem to make any right angle triangles where I know two lengths.

k

 

[dirk_mec1]

Use the cosine rule.

 

[kenewbie]

Use the cosine rule.

I wanted a solution without trig.

But I just figured it out. A 90 degree angle has to be located on a circle with diameter equal to the hypothenus, and so the line must be equal to the radius of the circle, and so it is 2.5

k

 

[dirk_mec1]

I wanted a solution without trig.

But I just figured it out. A 90 degree angle has to be located on a circle with diameter equal to the hypothenus, and so the line must be equal to the radius of the circle, and so it is 2.5

k

Your answer is correct.

 

[Diffy]

You could have also just used Pythagorean theorem and a system of equations with 2 variables to work it out.

 

[Diffy]

Never mind my last post. I read the problem incorrectly. I thought the line was perpendicular to the hypotenuse, not at its midpoint.