What does the law of cosines reduce to when dealing with a right triangle?A.The formula for a triangle's areaB.The law of cosines cannot be applied to a right triangle.C.The law of sinesD.The Pythagorean theorem
Question
What does the law of cosines reduce to when dealing with a right triangle?A.The formula for a triangle's areaB.The law of cosines cannot be applied to a right triangle.C.The law of sinesD.The Pythagorean theorem
Solution
The law of cosines reduces to the Pythagorean theorem when dealing with a right triangle.
Here's why:
The law of cosines is given by the formula c² = a² + b² - 2abcos(C), where C is the angle opposite side c in a triangle.
In a right triangle, the angle C is 90 degrees. The cosine of 90 degrees is 0.
So, the law of cosines formula becomes c² = a² + b² - 2ab*0, which simplifies to c² = a² + b².
This is the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (side c) is equal to the sum of the squares of the lengths of the other two sides (sides a and b).
Similar Questions
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The law of cosines can only be applied to acute triangles.A.TrueB.False
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