Hi Friends! In this answer math problems for free session we will discuss about Special right triangle. A special right triangle is a right triangle having specific characteristics which make its calculations much easier or for which simple formulas exist. We can classify special right triangles in two categories: the angles of a right triangle may form some simple relationships, such as 45–45–90. The right triangles in this category are “angle-based" right triangle. Another category is on the basis of sides of the triangle, when the lengths of the sides form some ratios, and then those triangles are called “side-based" right triangles.
There are four types of special right triangles:
These two types come under side based special right triangles:
3–4–5 Triangles:
A 3-4-5 triangle is a special right triangle whose lengths of the sides are in the ratio of 3:4:5. The ratios can only be checked when you are given the lengths of any two sides of the triangle.
5–12–13 Triangle:
A 5-12-13 triangle is a special right triangle whose lengths of the sides are in the ratio of 5:12:13.
These two types come under angle based special right triangle (get more detail here):
45º45º90º right triangles or isosceles right triangle: An isosceles right triangle is a triangle having the characteristic of both isosceles and the right triangle as it has two equal angles, two equal sides, and one right angle. So the angles of an isosceles right triangle are 45°- 45°- 90°. Therefore the lengths of the sides of a 45°- 45°- 90° triangle are in the ratio of 1:1:√2.
A right angled triangle having two sides equal in length is called 45°- 45°- 90° triangle.
30º-60º-90º Triangles
A 30°- 60°- 90° right triangle is a special right triangle whose angles are 30°, 60°and 90° and therefore the lengths of the sides of a 30°- 60°- 90° triangle are in the ratio of 1:√3:2 .
In upcoming posts we will discuss about Planar cross-sections and Measures of central tendency in Grade XI. Visit our website for information on CBSE class 12 home science question bank
There are four types of special right triangles:
These two types come under side based special right triangles:
3–4–5 Triangles:
A 3-4-5 triangle is a special right triangle whose lengths of the sides are in the ratio of 3:4:5. The ratios can only be checked when you are given the lengths of any two sides of the triangle.
5–12–13 Triangle:
A 5-12-13 triangle is a special right triangle whose lengths of the sides are in the ratio of 5:12:13.
These two types come under angle based special right triangle (get more detail here):
45º45º90º right triangles or isosceles right triangle: An isosceles right triangle is a triangle having the characteristic of both isosceles and the right triangle as it has two equal angles, two equal sides, and one right angle. So the angles of an isosceles right triangle are 45°- 45°- 90°. Therefore the lengths of the sides of a 45°- 45°- 90° triangle are in the ratio of 1:1:√2.
A right angled triangle having two sides equal in length is called 45°- 45°- 90° triangle.
30º-60º-90º Triangles
A 30°- 60°- 90° right triangle is a special right triangle whose angles are 30°, 60°and 90° and therefore the lengths of the sides of a 30°- 60°- 90° triangle are in the ratio of 1:√3:2 .
In upcoming posts we will discuss about Planar cross-sections and Measures of central tendency in Grade XI. Visit our website for information on CBSE class 12 home science question bank
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