In a triangle XYZ , A is a point on XZ such that and angle XAY = 70 degrees. Find the length of XZ if angle XYZ = 110 degrees and YZ = 6cm
Please help me. Will Pythagoras work or do I need to use trigonometry? Or am I taking this too seriously and there is an easier method?
Did you mean XA/AZ=3? Because XA/AX=1.
I think this is even better than Pythagoras!
Similar triangles are everyone's friend!
Alright, I want you to find a piece of paper and a pencil or pen and draw the triangle.
I don't care if your book has it drawn already, just draw it.
Remember that angle XYZ=110, so make it obtuse.
Then, make point A so that the distance from A to X is about three times the distance from Z to A.
Now, label everything we know: angle XYZ, angle XAY, and side YZ.
But, we know something else! If angle XAY=70 and angle XAY+angle ZAY=180 (it's on a straight line), then angle ZAY=110.
Now, for the finale. Draw a second triangle. It should look that same as the first. The bigger angle is A.
This is a copy of the smaller triangle AYZ. Why? Well, we have similar triangles! angle ZAY=angle XYZ, and angle AZY=angle XZY.
From there, all you need to do is relate similar sides, and you're done.
Post back with what you think the answer is.
Ok, well I have done what you have said and the fact they are similar triangles has shocked me! (Bleesdan) I have also added the angle theta (mr fantastic) But how do I proceed after this? Do I split the 110 degree angle into 90 degree and 20 degree and use trigonometry?