To determine if the triangle with sides measuring 60 in., 75 in., and 45 in. is a right triangle, we can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
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Identify the lengths of the sides:
- \( a = 45 , \text{in} \)
- \( b = 60 , \text{in} \)
- \( c = 75 , \text{in} \) (hypotenuse, since it is the longest side)
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Apply the Pythagorean theorem:
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Calculate \( a^2 + b^2 \): \[ 45^2 + 60^2 = 2025 + 3600 = 5625 \]
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Calculate \( c^2 \): \[ 75^2 = 5625 \]
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Compare the two results:
- Since \( a^2 + b^2 = c^2 \) (i.e., \( 5625 = 5625 \)), the triangle satisfies the Pythagorean theorem.
Therefore, the triangle with sides measuring 60 in., 75 in., and 45 in. is a right triangle.
The correct response is: Yes, because 5,625 equals 5,625.