The legs of a right triangle are 5 cm and 12 cm long. Find the lengths, to the nearest tenth, of the segments into which the bisector of the right angle divides the hypotenuse.

Question

tkhunny · Answer

It is hoped that you first recognize the Pythagorean Triple, 5-12-13.  Check it out.  The hypotenuse is 13.

Go ahead and draw a picture.  Add to your usual right triangle, the andgle bisector of the Right angle and extend the bisector until it intersects the hypotenuse.

tkhunny · Answer

Label the sides, 5, 12, 13.  Don't worry too much about the scale.

tkhunny · Answer

Where's the 13?

anonymous · Answer

is it

anonymous · Answer

|dw:1364087734160:dw|

tkhunny · Answer

Yes.

Add the little angle to signify a Right angle and then label the angle to the right $\alpha$.  Finally, lable the top angle $\beta$

anonymous · Answer

okay wait so add 12 and 5 together?

anonymous · Answer

thats why i was confused

tkhunny · Answer

Why on EARTH would you do that?  Just label the angles.

tkhunny · Answer

Well, do the labeling.  Maybe that's why you're struggling.  Let the notation keep track of things for you.

anonymous · Answer

okay I labeled my drawing then what? Im sorry! Im really confused

tkhunny · Answer

Have a little faith.  Is thast lower-right angle labled $\alpha$ ?

anonymous · Answer

no?

tkhunny · Answer

Why not?  Label it.  Label it "Fred" if you like.  Just label it and show me what it is.  Label the one at the top, too.

anonymous · Answer

label them what? thats what I dont get! I wrote the number out so whats the labels for?

anonymous · Answer

sorry I just really dont know what im doing (obviously)

tkhunny · Answer

|dw:1364088286099:dw|

anonymous · Answer

oh my gosh okay gotcha

tkhunny · Answer

We just need a way to talk about the parts of the triangle.

anonymous · Answer

okay gotcha now sorry!

tkhunny · Answer

What do you know about angle "a"?

Homefully, $\tan(a) = 12/5$.  Agreed?

tkhunny · Answer

* hopefully

anonymous · Answer

okay

tkhunny · Answer

Can you find angle 'a'?  Tangent button on your calculator, maybe.

Whoops!  I have to go.

Find 'a'.  Then angle b = 90 - a.  You tell me why.  Once you get the measures of angles a and b, we can move on with the angle bisector.  Someone will help you, or I'll be back in a while.

anonymous · Answer

okay thanks....

tkhunny · Answer

Did you find the measures of angles a and b?

anonymous · Answer

I dont know haha I finished it already not sure what I even got but I think I got it...