A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle. The right triangle plays an important role in trigonometry. Let us learn more about this triangle in this article. Show
What is a Triangle?A triangle is a regular polygon, with three sides and the sum of any two sides is always greater than the third side. This is a unique property of a triangle. In other words, it can be said that any closed figure with three sides and the sum of all the three internal angles is equal to 180°. Being a closed figure, a triangle can have
different types and each shape is described by the angle made by any two adjacent sides. Types of Triangles
The other three types of triangles are based on the sides of the triangle.
Note: A scalene triangle and an isosceles triangle both can be a right triangle. A scalene right triangle will have all three sides unequal in length and any of the one angles will be a right angle. An isosceles right triangle will have its base and perpendicular sides equal in length, which includes the right angle. The third unequal side will be the hypotenuse. Watch The Below Video To Learn More About the Types of TrianglesA right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle. The third side is called the hypotenuse, which is the longest side of all three sides. The three sides of the right triangle are related to each other. This relationship is explained by Pythagoras theorem. According to this theorem, in a right triangle, Hypotenuse2 = Perpendicular2 + Base2 See the figure below to understand better. The area of the biggest square is equal to the sum of the square of the two other small square areas. We can generate the Pythagoras theorem as
the square of the length of the hypotenuse is equal to the sum of the length of squares of base and height. Shape of Right TriangleA right triangle is a three-sided closed shape, that has one perpendicular side called the leg or height of the triangle. Right Angle Triangle PropertiesLet us discuss, the properties carried by a right-angle triangle.
Area of Right Angle Triangle = ½ (Base × Perpendicular)
Above were the general properties of the Right angle triangle. The construction of the right angle triangle is also very easy. Keep learning with BYJU’S to get more such study materials related to different topics of Geometry and other subjective topics. Area of Right Angled TriangleThe area is in the two-dimensional region and is measured in a square unit. It can be defined as the amount of space taken by the 2-dimensional object. The area of a triangle can be calculated by 2 formulas: \(\begin{array}{l}Area= \frac{a \times b }{2}\end{array} \) And, Heron’s formula \(\begin{array}{l}Area= \sqrt{s(s-a)(s-b)(s-c)}\end{array} \) Here, s is the semi perimeter and is calculated as: \(\begin{array}{l}s =\frac{a+b+c}{2}\end{array} \) Where, a, b, c are the sides of a triangle. Let us calculate the area of a triangle using the figure given below. Fig 1: Let us drop a perpendicular to the base b in the given triangle. Fig 2: Now let us attach another triangle to a side of the triangle. It forms the shape of a parallelogram as shown in the figure. Fig 3: Let us move the red coloured triangle to the other side of the parallelogram as shown in the above figure. Fig 4: It takes up the shape of a rectangle now. Now by the property of area, it is calculated as the multiplication of any two sides Hence, area =b × h (for a rectangle) Therefore, the area of a right angle triangle will be half i.e. \(\begin{array}{l}Area = \frac{b \times h}{2}\end{array} \) For a right-angled triangle, the base is always perpendicular to the height. When the sides of the triangle are not given and only angles are given, the area of a right-angled triangle can be calculated by the given formula: \(\begin{array}{l}Area = \frac{bc \times ba}{2}\end{array} \) Where a, b, c are respective angles of the right-angle triangle, with ∠b always
being 90°. PerimeterAs we know, the three sides of the right triangle are Base, Perpendicular and Hypotenuse. Thus the perimeter of the right triangle is the sum of all its three sides. Perimeter of right triangle = Length of (Base + Perpendicular + Hypotenuse) Example: If Base =4cm, Perpendicular= 3cm and Hypotenuse = 5cm. What is the perimeter of right triangle? Perimeter
= 4 + 3 + 5 = 12 cm Solved ExamplesQ.1: In a right triangle, if perpendicular = 8 cm and base = 6 cm, then what is the value of hypotenuse? Solution: Given, Perpendicular = 8 cm Base = 6cm We need to find the hypotenuse. By Pythagoras theorem, we know that; Hypotenuse = √(Perpendicular2 + Base2) H = √(62 + 82) = √36 + 64 = √100 = 10 cm Therefore, the hypotenuse of the right triangle is 10 cm. Q.2: If the hypotenuse is 13 cm and the base is 12 cm, then find the length of perpendicular of the right triangle? Solution: Given, Hypotenuse = 13 cm Base = 12 cm Perpendicular = ? By Pythagoras theorem, we know that, Hypotenuse2 = Perpendicular2 + Base2 Perpendicular2 = Hypotenuse2 – Base2 P = √(132 – 122) P = √(169 – 144) P = √25 P = 5 cm Therefore, the value of perpendicular is 5cm. Practice Problems
To learn more interesting facts about triangles stay tuned with BYJU’S. Frequently Asked Questions From Right Angle TriangleRight-angled triangles are those triangles in which one angle is 90 degrees. Since one angle is 90°, the sum of the other two angles will be 90°. For a right-angled triangle, trigonometric functions or the Pythagoras theorem can be used to find its missing sides. If two sides are given, the Pythagoras theorem can be used and when the measurement of one side and an angle is
given, trigonometric functions like sine, cos, and tan can be used to find the missing side. No, a triangle can never have 2 right angles. A triangle has exactly 3 sides and the sum of interior angles sum up to 180°. So, if a
triangle has two right angles, the third angle will have to be 0 degrees which means the third side will overlap with the other side. Thus, it is not possible to have a triangle with 2 right angles. For any
triangle, the sum of all the interior angles is equal to 180 degrees. The three sides of a right triangle are base, perpendicular and hypotenuse. How do you find an angle of a triangle with 3 sides?To solve an SSS triangle: use The Law of Cosines first to calculate one of the angles. then use The Law of Cosines again to find another angle. and finally use angles of a triangle add to 180° to find the last angle.
What is the formula to find the angle of a right triangle?The formula used for a right-angled triangle is the Pythagoras formula. It states the square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagoras formula is (Hypotenuse)2 = (Base)2< + (Altitude)2. This formula has given the Pythagoras triplets such as 3, 4, 5.
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