About Special Right Triangles
Special right triangles are right-angled triangles with fixed interior angles and sides that always have the same ratio. There are two kinds of special right triangles: one with angles of 45°, 45°, and 90°, and the other with angles of 30°, 60°, and 90°.
What do you mean by Special Right Triangles?
Special right triangles are those with all three internal angles determined and a fixed ratio between the sides. If one side is given, we can find the value of two missing sides in these right-angled triangles. The 45°- 45°- 90° triangle and the 30°- 60°- 90° triangle are the two exceptional right triangles. Let us review the essential features of a right triangle before going into further detail:
- One of the angles in a right triangle is 90 degrees, and the total of the other two angles equals 90 degrees.
- The hypotenuse is the triangle's longest side and is the side opposite the right angle.
45° 45° 90° triangle
Because two of its acute angles are identical to 45 degrees, a 45° 45° 90° triangle is an isosceles right triangle. The following is the ratio of its legs to hypotenuse: Hypotenuse = 1: 1: √2. Leg: Leg It can be represented in terms of x as x: x: x√2, as shown below.
30° 60° 90° triangle
The acute angles of a 30 - 60 - 90 triangle are 30° and 60°, respectively. The following is the ratio of its legs to hypotenuse: Leg length: Long leg: 1: √3: 2 Hypotenuse. It can be represented in terms of x as x: x√3: 2x, as shown below.
Special Right Triangle Formula
The right triangle formula is the Pythagoras theorem formula that states that the square of the hypotenuse in a right-angled triangle equals the sum of the squares of the other two sides. In the case of exceptional right triangles, however, we apply specific ratios that act as formulas, allowing us to calculate the missing sides of a triangle even when only one side is known. The ratio formulas for the special right triangle formulas are as follows:
30° 60° 90° triangle formula: Short leg: Long leg : Hypotenuse = x: x√3: 2x
45° 45° 90° triangle formula: Leg : Leg: Hypotenuse = x: x: x√2
To get the list of Maths formulas check out the main page.
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