Thank you for visiting Triangle ABC has the following measures m angle A 46 circ m angle B 73 circ text and b 32 3 What is the length. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
By applying the Law of Sines to the given information about triangle ABC, we find that none of the provided options match the calculated value for side c. There seems to be a mistake in the options provided. none of the option is correct
Explanation:
To determine the length of side c in triangle ABC, given m ∠ A = 46 ∘ , m ∠ B = 73 ∘ , and side b = 32.3 , we would need to apply the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
The missing angle C can be found using the fact that the sum of angles in a triangle is 180 degrees. To find the length of side c, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides and their opposite angles in a triangle.
Therefore, ∠ C = 180 - 46 - 73 = 61 degrees. Applying the Law of Sines we get: b/sin(B) = c/sin(C), so c = b*sin(C)/sin(B) = 32.3*sin(61)/sin(73). Upon calculation, we do not get any of the provided options a. 35.9 b. 24.3 c. 29.5 d. 61.0 as the answer. Therefore, there seems to be an error in the given choices. none of the option is correct
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