geometry question plz help?

Question

okay how are u suppose to find the height of a rigt triangle if ur only given the legs and the hyp.?

heres a pic of the problem for the first guy that answered:

http://i130.photobucket.com/albums/p271/liers_sux/campix.jpg

Answer 1

I wouldn't be at all surprised if the "height" we're trying to find here is the perpendicular distance from the right angle to the hypotenuse.

Let's say you have right triangle ABC, with C being the right angle. Let D be the projection of C onto AB. Since angle A is common to triangles ABB and ACD and they both have a right angle, triangle ABC is similar to triangle ACD. This means that BC/AB=CD/AC or CD=AC*BC/AB.

For example in a 3,4,5 right triangle, the perpendicular from the right angle to the hypotenuse is 3*4/5 or 12/5.

(Geez... I take 15 to answer this and couple people sneak in ahead of me. :-) )

Answer 2

Actually each leg is a height (or more accurately an altitude). But I think you want the one that uses the hypotenuse as the base. This height (altitude) is the product of the legs divided by the hypotenuse. For a 3 - 4 - 5 right triangle, the two legs are both heights (altitudes), and the one that divides the right angle is (3 * 4) / 5 or 2 2/5 for this example.

Answer 3

according to the pythagorrean(sp) theorem a^2+b^2=c^2. this works for all right triangles. the legs are a and b. and c is always the hypotenuse. so if one leg is 3 and the hypotenuse is 5 and you wanted to know the lenghth of the other leg (the height) then you would have 3^2 + b^2 = 5^2. so 9 + b^2 = 25. so b^2 = 16. and b =4. i hope this makes sense.

Answer 4

You can use trigonmetry, but if you don't have that, you can use some sneaky algebra.

I assume the triangle rests on its hypotenuse and the right angle is "up in the air". Call the hypotenuse AB and the right angle ACB. Now drop the altitude from angle ACB to AB and call it CD. CD cuts the hypotenuse into two parts, lets call AD= h-x and DB=x.
Then (h-x)^2+CD^2 = AC^2
x^2 + CD^2 = CB^2
But AC^2 + CB^2 = h^2, so we can add both equations to get:
2 CD^2 = h^2+x^2+(h-x)^2

Answer 5

apply pythagoras theorem
( hypotenuse)^2 = (base(leg))^2 + height^2
therfore , height^2 = ( hypotenuse)^2 - (base(leg))^2

PS: by the way, I wonder what you mean by legs. A triangle has only three sides, one is the hypotenuse,one is the height , one is the base (your leg in this question) , where does the question of leg's' come from??