What is a Right Angle?
When a vertical line and a horizontal line intersect, a right angle is formed at the point of intersection. The vertical line is also named as the perpendicular line, and the horizontal line is also named as the base line. We can observe many real-life examples of right angles in our daily life.
- Corners of a wall
- L-shaped sofas
- Edges of windows and doors
- Corners of laptops
- Intersection of roads
Definition of a Right Angle
A right angle is formed by the intersection of two rays. The unit of measurement of an angle is ‘degree’, and if the measure of an angle is 90°, it is called a right angle. Right angles always appear as an ‘L’ shaped angle. In the image shown, \(\angle~AOB~=~90^\circ \).
Right Angle Triangle
A right-angled triangle has three sides, a base leg, a hypotenuse leg and a perpendicular leg. The angle between the base and the perpendicular is 90°. A right-angled triangle is also one of the most basic shapes in geometry, and it forms the foundation for trigonometry.
In a right angle triangle, the hypotenuse is the longest side and angles opposite to it is the right angle of the triangle.
Properties of a Right Angle Triangle
- One angle of a right angle triangle is always 90° or a right angle
- The side opposite to the 90° angle is the hypotenuse
- The hypotenuse is the longest side of a right angle triangle
- The sum of the other two interior angles is equal to 90°
- The other two sides adjacent to the right angle are called the base leg and the perpendicular leg
- The area of a right-angle triangle is equal to half of the product of the adjacent sides of the right angle,
Area of Right Angle Triangle = \(\frac{1}{2} \) (Base × Perpendicular)
- If one of the angles is 90° and the measure of other two angles are equal to 45° each, then this triangle is called an ‘Isosceles Right Angled Triangle’, in which the adjacent sides to the 90° angle are equal in length.
Solved Examples on Right Angle
Example 1: Write three names of the angle given below.
Solution:
Three names of the angles are
\(\angle~AOB~=~90^\circ \), \(\angle~BOA~=~90^\circ \) and \(\angle~O~=~90^\circ \).
Since it is an L shaped angle, it is a right angle.
Example 2: You have a circular crafted dining table. You divide the table into four equal sections. What is the measure of each angle formed at the center of the table ?
Solution:
The angle formed by the dining table is \(360^\circ \). Here, we have to divide \(360^\circ \) into four equal parts to get the measure of each angle formed at the center of the table.
\(360~\div~4 \) = \(90^\circ \)
Hence, the measure of each angle formed at the center of the table is \(90^\circ \) .
Example 3: Find the angle formed by the clock at 3 pm and 9 pm.
Solution: We can see from the watch that at 3 pm and 9 pm the hour hand and the minute hand form an L shape. When the shape is L the angle formed is \(90^\circ\).
Hence, the angle formed by the clock at 3 pm and 9 pm is \(90^\circ\).
There are three 30 degree angles in a right angle.
Straight angle indicates that the measure is 180 degrees. Hence, when we divide 180 degrees by 2 we will get two right angles.
When the sum of any two angles is 90 degrees, then these two angles are called complementary angles.
Right-angled triangles are triangles in which one of the angles is 90 degrees. Since one angle is 90 degrees, the sum of the other two angles will be 90 degrees.