Urgent geometry help?

Question

There is right triangle ABC with sides measuring p, q & hypotenuse r. Find the length of the altitude from B to hypotenuse AC in terms of p,q and r.

I know the answer is pq/r but I don't know how to get it. I'm looking for well explained answers. Please help.

Answer 1

IF U CAN USE TRIGONOMETRY IT IS VERY EASY !!!

Name the point as D wher the altitude meets hyp AC

Now sin of angle C = p/r (for triangle ABC)

And sin of angle C = BD/q (for triangle BDC)

SO p/r = BD/q

BD = pq/r

Answer 2

The altitude you have described splits the triangle into two other similar triangles similar to the original. Draw the original so that p is the shorter leg and q is the longer leg. Put x on the side drawn and write a proportion involving x, p, q and r.

In the original triangle, q is the longer leg and r is the hypotenuse. In the triangle containing x and p, x is the long leg and p is the hypotenuse.

So q/r = x/p

Cross multiply rx = pq

Divide both sides by r: x = pq/r

Answer 3

That line is called an altitude (off of side AC to the right angle) and it forms two similar triangles, which are also similar to the original triangle.

So you can create ratios.
Let x be the altitude. The ratio of x to side p is the same as side q to the hypotenuse (r)

x/p = q/r

Now solve for x:

x = pq/r

Answer 4

I took gemotery last year with a stupid teacher so I didnt get anything sorry Cant help u