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I'm struggling with my geometry class, specifically with the topic of special right triangles (30-60-90 and 45-45-90). Can someone explain their ratios and any useful tips to remember them? Thanks in advance!

5 months ago

Sure, I'd be happy to help with special right triangles! There are two types of special right triangles you've mentioned: 30-60-90 and 45-45-90. Let's break them down.

1. 30-60-90 triangle:

In a 30-60-90 triangle, the angles are 30 degrees, 60 degrees, and 90 degrees. The ratio of the side lengths of this triangle is 1:√3:2. Here's what this means:

- The side opposite the 30-degree angle (shortest side) has length x (we'll call this the "base").

- The side opposite the 60-degree angle has length x√3 (we'll call this the "height").

- The side opposite the 90-degree angle (the hypotenuse) has length 2x.

Remembering this ratio can be helpful for solving problems involving 30-60-90 triangles.

2. 45-45-90 triangle:

In a 45-45-90 triangle, both non-right angles are equal (45 degrees) since its a right isosceles triangle; the other angle, of course, is 90 degrees. The ratio of the side lengths for this triangle is 1:1:√2. Here's how it breaks down:

- The sides opposite the two 45-degree angles (the legs) are equal in length, and we'll call them x.

- The side opposite the 90-degree angle (the hypotenuse) has a length x√2.

Remembering this ratio can be helpful for solving problems involving 45-45-90 triangles.

Here's a helpful tip to remember these ratios: for the 30-60-90 triangle, think "smallest angle, smallest side (x); biggest angle, biggest side (2x), and medium angle, medium side(x√3)." For a 45-45-90 triangle, remember that "45" is half of "90," so the legs are equal, and the hypotenuse has a length equal to one of the legs multiplied by √2.

Practice solving problems with these ratios, and you'll become more comfortable using these properties of special right triangles. Good luck with your geometry class!

5 months ago

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