Examples on Right Angled Triangle
Let’s solve some example problems on right angled triangles.
Example 1: Find the area of a triangle if the height and hypotenuse of a right-angled triangle are 10 cm and 11 cm, respectively.
Solution:
Given:
- Height = 10 cm
- Hypotenuse = 11 cm
Using Pythagoras’ theorem,
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
(11)2 = (Base)2 + (10)2
(Base)2 = (11)2 – (10)2 = 121 – 100
Base = √21 = 4.6 cm
Area of the Triangle = (1/2) × b × h
Area = (1/2) × 4.6 × 10
Area = 23 cm2
Example 2: Find out the area of a right-angled triangle whose perimeter is 30 units, height is 8 units, and hypotenuse is 12 units.
Solution:
- Perimeter = 30 units
- Hypotenuse = 12 units
- Height = 8 units
Perimeter = base + hypotenuse + height
30 units = 12 + 8 + base
Base = 30 – 20 = 10 units
Area of Triangle = 1/2×b×h = 1/2 ×10 × 8 = 40 sq units
Example 3: If two sides of a triangle are given find out the third side i.e. if Base = 3 cm and Perpendicular = 4 cm find out the hypotenuse.
Solution:
Given:
- Base (b) = 3 cm
- Perpendicular (p) = 4 cm
- Hypotenuse (h) = ?
Using Pythagoras theorem,
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
= 42 + 32 = 16 + 9 = 25 cm2
Hypotenuse = √(25)
Hypotenuse = 5 cm
Important Maths Related Links:
Right Angled Triangle | Properties and Formula
Right Angled Triangle: A triangle is a polygon with three sides, three vertices, and three angles thus, the name Triangle. A right-angled triangle is a triangle with one right angle (90°). Right Angle Triangle plays a very important role in trigonometry.
In this article, we will learn about the right-angled triangle, including Right Angled Triangle definition, perimeter, area, right-angled triangle formula, and Right Angled Triangle properties in detail.
Table of Content
- What is a Right Angled Triangle?
- Right Angled Triangle Definition
- Properties of Right Angled Triangle
- Right Triangle Formula
- Perimeter of Right Angled Triangle
- Right Angled Triangle Perimeter Formula
- Right Angled Triangle Area Formula
- Derivation of Right Angled Triangle Area Formula
- Hypotenuse of Right Angled Triangle
- Examples on Right Angled Triangle