Thank you for visiting The distance between two locations A and B is calculated using a third location C at a distance of 15 miles from location B If. 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:
To find the distance between locations A and B, use trigonometry and the law of sines. Angle A can be found by subtracting angles B and C from 180°. Then, use the law of sines to find the length of AB.
Explanation:
To find the distance between locations A and B, we can use the concept of trigonometry and law of sines. Let's consider the triangle ABC. Angle B is given as 105° and angle C is given as 20°. Since the sum of angles in a triangle is 180°, we can find angle A by subtracting angles B and C from 180°. So, angle A = 180° - 105° - 20° = 55°.
Now, we can use the law of sines to find the length of AB. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In this case, we can use the ratio AB/sin(B) = BC/sin(A) to find AB. Plugging in the values, we get AB/sin(105°) = 15/sin(55°).
Solving this equation, we find AB ≈ 35.9 miles. So, the correct answer is (b) 35.9 miles.
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