Differentiating between 30-60-90 and 45-45-90

GRE Quant Problem Solving
1

Hey y’all,
I’m watching the tips and tricks video and I’m having difficulty figuring out when the triangle is 30-60-90 vs when it’s a 45-45-90. For example, if you’re given a triangle with the shortest side and the 90-degree indicator, but no other info, how do you know which shortcut to use??
Thanks in advance!

2

if both p and b are equal then this triangle might be 45-45-90 but in another case, you have to verify yourself.

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Khan Acadmeny videos for bothhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/a/special-right-triangles-review

30-60-90 https://blog.prepscholar.com/30-60-90-triangle-ratio-formula
45-45-90https://www.dummies.com/education/math/geometry/identifying-the-45-45-90-degree-triangle/

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4

This is interesting.
45-45-90 has 2 sides equal and 2 angles equal each other.
Side length is in ratio of x:x:x*sqrt(2)
One important rule in triangles is that:
*Equal sides always correspond equal angle.

In 30-60-90, the length of sides do not equal to each other. In addition, the side that face 60 angle is always bigger than the other side.
Sides length is in ratio of x:x*sqrt(3)*2x
Hope it helps

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