OG p. 260 #8

[Alexander]

Hi -

How do you solve this? There isn't an explanation, just the answer on p. 262.

My thoughts:

I thought using 1:sq(3):2 would work, but you can't tell if it's a 30:60:90 or 45:45:90. So it could be 1:1:sq(2) instead.

I determined the base is 50 ( 40 +10 ), and have one piece to the pythag theorem to solve this equation.

ON = 24 + X, I tried to make a right triangle to find the small piece of the hypotenuse we aren't given. But that didn't work

So I'm stuck...

Thanks

[Alexander]

Correct me if I'm wrong, but the key is the 'similarity' rules of triangles. So...

A right triangle within a right triangle = Similar!

You just need to set up the right proportions just like #7 of the OG Math Review p. 260

[n00bpron00bpron00b]

Hey,

I think the concept of similar triangles works fine

Angle P is common to both
One angle is 90
So the third angle has to be same

Length ON = 30 (by setting up a proportion)
OP = 10 sqrt 34 (Pythagorean theorem)

[tommywallach]

Yep! Recognizing the similarity of the three triangles is the key here.

-t