Question

A triangular earring has side lengths of 1.5 centimeters, 2 centimeters, and 3 centimeters. What is the approximate measure, in degrees, of the largest angle of the triangular earring? A. 36.3° B. 45.8° C. 117.3° D. 134.2°

Answer 1

To find the largest angle of a triangular earring with given side lengths, we can use the Law of Cosines. Plugging in the values and solving for cos(C), we find that the largest angle is approximately D)134.2 degrees.

Step-by-step explanation:

To find the largest angle of a triangular earring, we need to use the Law of Cosines. Let's label the sides of the triangle as a, b, and c with c being the longest side. Using the formula:
c^2 = a^2 + b^2 - 2ab*cos(C)
where C is the angle opposite side c, we can substitute the given side lengths to find the measure of the largest angle. Plugging in the values, we have:
3^2 = 1.5^2 + 2^2 - 2(1.5)(2)*cos(C)
Simplifying and solving for cos(C), we get:
cos(C) = -0.625
Taking the inverse cosine of -0.625, we find that C is approximately 134.2 degrees.

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