There are two types of special right triangles and they have the following properties:

The first one is the 45

Let's call the longest side Hypothenuse. Using the pythagorean theorem, we get

Hypothenuse

Hypothenuse

Let's take the square root of both sides

√(Hypothenuse

Hypothenuse = √(2)×√(Leg

So, the formula is:

Well, it is a shortcut to solve problems. If the legs of a right triangle are equal, you can quickly find the length of the legs or the hypothenuse given the length of the hypothenuse or the length of a leg respectively

The legs of an isosceles right triangle measure 10 inches. Find the length of the hypothenuse.

Since the triangle is isosceles, the legs are equal and we can use the formula

Hypothenuse = √(2)×(Leg)

Hypothenuse = √(2)×(10)= 14.1421 inches

The second type of special right triangles is the 30

Using the pythagorean theorem, we get

Hypothenuse

(2 × Short Leg)

(2 × Short Leg)×(2 × Short Leg) = (Short Leg)

(4 × (Short Leg)

4 × (Short Leg)

4 × (Short Leg)

4 × (Short Leg)

3 × (Short Leg)

Let's take the square root of both sides

√(3 × Short Leg

(√3) × √((Short Leg)

(√3) × (Short Leg) = Long Leg

So, the formula for the long leg is:

(√3) × 1/2(Hypothenuse)

The Hypothenuse of a 30

Short Leg = 1/2 × (Hypothenuse) = 1/2 × 20 = 10 inches

Long leg = (√3) × Short Leg = √3) × 10 = 17.32 inches

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