Answer:
Step-by-step explanation:triangle P: 12, 24, and 30
triangle Q: 9, 40, and 41
triangle R: 5, 18, and 21
Which triangle is a right triangle? Explain your reasoning.
The triangle Q is a right triangle because it respects the Pythagoras Theorem.
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. In this triangle from the trigonometric ratios or the Pythagoras Theorem ([tex]hypotenuse^2=(side_1)^2+(side_2)^2[/tex]), it is possible finding angles or sides. It is important to know that the hypothenuse is the greatest side of a right triangle.
Here the hypotenuse is equal to 30. Then,
[tex]hypotenuse^2=(side_1)^2+(side_2)^2\\ \\ 30^2=24^2+12^2\\ \\ 900=576+144\\ \\ 900\neq 720[/tex]
It is not a right triangle.
Here the hypotenuse is equal to 41. Then,
[tex]hypotenuse^2=(side_1)^2+(side_2)^2\\ \\ 41^2=9^2+40^2\\ \\ 1681=81+1600\\ \\ 1681=1681[/tex]
It is a right triangle.
Here the hypotenuse is equal to 21. Then,
[tex]hypotenuse^2=(side_1)^2+(side_2)^2\\ \\ 21^2=5^2+18^2\\ \\441=25+324\\ \\ 441\neq 349[/tex]
It is not a right triangle.
Learn more about Pythagoras theorem here:
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