Questions: Calculate the side lengths a and b to two decimal places. A. a=4.81 and b=5.33 B. a=16.23 and b=17.99 C. a=16.23 and b=18.83 D. a=17.99 and b=16.23 E. a=5.33 and b=4.81

Calculate the side lengths a and b to two decimal places. A. a=4.81 and b=5.33 B. a=16.23 and b=17.99 C. a=16.23 and b=18.83 D. a=17.99 and b=16.23 E. a=5.33 and b=4.81
Transcript text: 4.3.3 Quiz: Law of Sines and Proofs Question 10 of 10 Calculate the side lengths $a$ and $b$ to two decimal places. A. $a=4.81$ and $b=5.33$ B. $a=16.23$ and $b=17.99$ C. $a=16.23$ and $b=18.83$ D. $a=17.99$ and $b=16.23$ E. $a=5.33$ and $b=4.81$
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Solution

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Solution Steps

Step 1: Find the missing angle

The sum of angles in a triangle is 180°. We are given two angles, 64° and 85°. Thus, the third angle is 180° - 64° - 85° = 31°.

Step 2: Use the Law of Sines to find side a

The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C). We are given side c = 9.3 and angle C = 31°. We want to find side a, and we know angle A = 64°. So, a/sin(64°) = 9.3/sin(31°). Therefore, a = 9.3 * sin(64°) / sin(31°) ≈ 16.23.

Step 3: Use the Law of Sines to find side b

We can use the Law of Sines again to find side b. We know angle B = 85°. So, b/sin(85°) = 9.3/sin(31°). Therefore, b = 9.3 * sin(85°) / sin(31°) ≈ 17.99.

Final Answer: The correct answer is B. a = 16.23 and b = 17.99.

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