I have this image and I need to find out the height of the triangle.

What I know:

• The triangle is rectangular so that angle above is 90º
• The base of the triangle is 50 ( sqroot(40²+30²) ).

I need to find out height (please without really advanced stuff, if I were in USA, I'd be highschool freshman, so something about that level).



The triangle can also be divided in two rectangular triangles.

EDIT: Also, no trigonometry. I know how to use it, but can't use it this year.

Seems like you can split that triangle in half and use the Pythagorean Theorem.

No, that can't because he doesnt know the hight.

Ok if you split the triangle the hypotenuse is 30 and the bottom is 25. You can use the Pythagorean Theorem to find missing legs, too.

30²=x²+y²
40²=(50-x)²+y²

Got it, y is height, thanks much everyone though!

well, were is no need for advanced sin/cos-stuff... one can simply use the area of the triangle:
A = (50 * h)/2 = 30*40/2
which leeds to h = 24, if i'm not mistaken

I have no idea of what you did Horrowind :S

Solving my system of equations:

30²=x²+y²
40²=(50-x)²+y²
I get x=18 and y=24, which is exactly the answer (24).

@Builderbot: I tried trigonometry but I couldn't do it because I don't know how to find out the two lower angles. Did you make it? I'd like to know a sin/cos solution too.

Quote from: Horrowind on May 05, 2011, 03:49:40 pm

well, were is no need for advanced sin/cos-stuff... one can simply use the area of the triangle:
A = (50 * h)/2 = 30*40/2
which leeds to h = 24, if i'm not mistaken

Mind explaining? I'm curious to know why the area is the same as the height

It isn't, the area can be calculated by:

(b*h)/2    ;b=50 and h=24
(50*24)/2
A = 600


So i made a new picture to name the angles, there is angle A,B,C and D.  We first need to find angle B.  Sin = opposite over the hypotenuse.  In triangle ABC, the hypotenuse is 50, and the opposite of angle B is 40.  So Sin(B)=40/50.  

Now we also have triangle ABD, where 30 is the hypotenuse, and side Y is the opposite to angle B.  So in this case, Sin(B) = Y/30.  

Now we substitute both equations for Sin(B) and get 40/50 = Y/30.  Solving yields 24.