Question

Help! This is due soon!

Answer 1

What are special right triangles?

Special right triangles are triangles that maintain a standard side length ratio. They are

• 45°-45°-90° triangles
• 30°-60°-90° triangles

In 45°-45°-90° triangles, the side length ratio follows a 1:1:√2 format [also written as x:x:2x], where the two legs of the triangle are the same length and the hypothenuse is the side length number × √2.

ex: 2:2:2√2

In 30°-60°-90° triangles, the side length ratio follows a 1:√3: 2 ratio [also written as x:x√3:2x] , where the shortest leg of the triangle is 1, the longest leg of the triangle is √3, and the hypothenuse is 2

ex: 2: 2√3: 4

In this example, the two legs are not the same length. If they were both of the numbers would be the same. However, they are 1 and √3. This means it is a 30°-60°-90° triangle. Now knowing this, you know that the hypothenuse will ×2 the shortest leg [2x],. 2×1 = 2.

2 is the length of the third side

Answer 2

2

Explanation:

Use pythagorean theorem:

`a^2+b^2=c^2`

Substitute in the values:

`√(3)^2+1^2=c^2`

square root and squared cancel each other out

`3+1^2=c^2`

square the b value

`3+1=c^2`

simplify

`4=c^2`

take square root of both sides

`2=c\\c=2`

So, the 3rd side length is 2.

Hope this helps! :)