A right triangle (or right-angled triangle) is a type of triangle where one of the angles is exactly 90 degrees. This unique geometric shape forms the basis of many fundamental concepts in mathematics, especially trigonometry. Below, we delve into the definitions, properties, and formulas associated with right triangles, presented in a clear and engaging manner.
A right triangle consists of:
A triangle with all side lengths as integers is called a Pythagorean triangle, and these side lengths form a Pythagorean triple.
The relationship between the sides of a right triangle is given by the famous Pythagoras Theorem:
c2=a2+b2c^2 = a^2 + b^2
Where:
For a triangle with sides a=3a = 3, b=4b = 4, and c=5c = 5: 52=32+425^2 = 3^2 + 4^2 25=9+1625 = 9 + 16
This verifies the theorem.
Below are common Pythagorean triples where all sides are integers:
The area of a right triangle is: Area=12×a×b\text{Area} = \frac{1}{2} \times a \times b Where aa and bb are the legs.
If an altitude is drawn from the right-angle vertex to the hypotenuse:
The radius rr of the incircle of a right triangle is: r=a+b−c2r = \frac{a + b – c}{2}
The circumradius RR is half the length of the hypotenuse: R=c2R = \frac{c}{2}
In a right triangle:
Right triangles appear in:
Conclusion
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