Math Doubts

Right triangle

A triangle which contains right angle as one of its angles is called a right triangle or right angled triangle.

Introduction

The meaning of right triangle is defined by combining the meanings of right angle and triangle. A right angle represents $90$ degrees. So, if any triangle contains right angle as one of its angles, then the triangle is called a right angled triangle and simply called as right triangle in geometric mathematics.

Sides

Right triangle is a very special triangle. So, each side of this type of triangle is called by a special name.

sides of right triangle

Adjacent side

A side which acts as a base of the triangle is called adjacent side and it is also called as base.

Opposite side

A side which makes a right angle with adjacent side is called opposite side.

Hypotenuse

A side that joins end points of both opposite and adjacent sides is called hypotenuse.

Angles

In a right triangle, three interior angles are formed by the intersection of the sides. An angle is a right angle and the remaining two angles are complementary angles.

angles of right triangle

Right angle

The angle between opposite side (perpendicular) and adjacent side (base) is a right angle.

$\angle BAC$ is right angle in this right triangle. So, $\angle BAC = 90^\circ$.

Angle of right triangle

The angle between adjacent side (base) and hypotenuse is called angle of right triangle. It is quite opposite to the opposite side of the triangle.

In this example, $\angle ABC$ is angle of right triangle.

Other angle

There is an angle between hypotenuse and opposite side (perpendicular). It is $\angle BCA$ and also a complementary angle of angle of right triangle. So, it can be calculated by using formula of complementary angles.

$\angle BCA = 90^\circ-\angle ABC$

Properties



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