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Question 9 • Mathematics III

On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: A squared is equal to b squared plus c squared minus 2 b c cosine cap A

Answer

Image with description X Y Z is a triangle, right angled at Y. The length of the sides X Y, Y W, and W X are labeled as a, 9, and y.

Image with description Triangle W X Y is shown. The length of the sides X W and X Y are congruent. The length of the side W Y is 7.

Image with description Triangle X W Y is shown. The length of the sides X Y, Y W, and W X are 8, 16, and 10.

Image with description Triangle X W Y is shown. The measure of the angle X Y W is 76 degrees. The length of the sides X Y, Y W, and W X are labeled as 5, 10, and y.

Explanation

To use the law of cosines directly to find an unknown angle, you need the lengths of all three sides. Choice C gives all three lengths: 8, 16, and 10, so you can substitute them into the formula and solve for an angle. Choice A gives an angle and two sides, while B and D do not provide three side lengths.

AI-written and checked against the verified answer.

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