Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.
In a right angled triangle,
According to Pythagoras theorem.
\[\left( \text{Hypotenuse} \right)^2 = \left( \text{Base} \right)^2 + \left( \text{Height} \right)^2 \]
\[ = \left( 9 \right)^2 + \left( 12 \right)^2 \]
\[ = 81 + 144\]
\[ = 225\]
\[ \therefore \text{Hypotenuse} = 15 cm\]
Hence, the length of the hypotenuse is 15 cm.
Concept: Apollonius Theorem
Is there an error in this question or solution?
13cm. Using Pythagoras theorem a^2 +b^2 =c^2 we substitute our two known lengths into the equation to get 5^2 + 12^2=c^2.
So now we have c^2= 25+144. So c^2 =169. So c=√169 = 13. Don't forget the units!!! So answer is 13cm
Write a Python program to calculate the hypotenuse of a right angled triangle. From Wikipedia, Pictorial Presentation: Sample Solution-1: Python Code :
A right triangle or right-angled triangle, or more formally an orthogonal triangle, is a triangle in which one angle is a right angle. The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the hypotenuse.
If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.
Sample Output:
Input lengths of shorter triangle sides: a: 3 b: 4 The length of the hypotenuse is: 5.0Visualize Python code execution:
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Sample Solution-2:
Python Code:
def test(x, y): h = (x**2 + y**2)**0.5 return h print(test(3,4)) print(test(3.5,4.4))Sample Output:
5.0 5.622277118748239Flowchart:
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Python Code Editor:
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