In this section we will discuss, Application On Pythagorean Theorem
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation. a^{2} + b^{2} = c^{2}
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
Application On Pythagorean Theorem is used to check whether the triangle is acute,obtuse or right.
A corollary of the Pythagorean theorem's converse is a simple means of determining whether a triangle is right, obtuse, or acute, as follows. Where c is chosen to be the longest of the three sides and a + b > c (otherwise there is no triangle according to the triangle inequality). The following statements apply:
If a^{2} + b^{2} = c^{2}, then the triangle is right.
If a^{2} + b^{2} > c^{2}, then the triangle is acute.
If a^{2} + b^{2} < c^{2}, then the triangle is obtuse.
Examples on Application On Pythagorean Theorem
Q.1 Determine which of them are right triangles, and if it is not right triangle then name the type of triangle.
1) a = 7 cm , b = 24 cm and c = 25 cm
Solution :
a^{2} + b^{2} = 7^{2} + 24^{2}
= 49 + 576
a^{2} + b^{2} = 625
c^{2} = 25^{2}
c^{2} = 25
From above,
a^{2} + b^{2} = c^{2}
∴ It is a right triangle.
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2) a = 9 cm , b = 16 cm and c = 18 cm
Solution :
a^{2} + b^{2} = 9^{2} + 16^{2}
= 81 + 256
a^{2} + b^{2} = 337
c^{2} = 18^{2}
c^{2} = 324
From above,
a^{2} + b^{2} > c^{2}
∴ It is an acute triangle.
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Q.2 Solve :
1) Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m. find the distance between their tops. Solution :
AB and ED are the two poles.