Greg and Lucy are standing on a riverbank, at points A and B respectively. (See the figure below.) Lucy is 230 meters from a house located across the river at point C. Suppose that angle A (angle BAC) is 47°, and angle B (angle ABC) is 75°. How far are Greg and Lucy standing from one another? Round your answer to the nearest tenth of a meter.47°75°ABC230mmeters CheckSave For LaterSubmit Assignment
Question
Greg and Lucy are standing on a riverbank, at points A and B respectively. (See the figure below.) Lucy is 230 meters from a house located across the river at point C. Suppose that angle A (angle BAC) is 47°, and angle B (angle ABC) is 75°. How far are Greg and Lucy standing from one another? Round your answer to the nearest tenth of a meter.47°75°ABC230mmeters CheckSave For LaterSubmit Assignment
Solution
To solve this problem, we can use 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.
In this case, we have a triangle ABC, where AC = 230 meters, ∠BAC = 47°, and ∠ABC = 75°. We want to find the length of AB.
According to the Law of Sines, we have:
AC/sin(∠ABC) = AB/sin(∠BAC)
Substituting the given values, we get:
230/sin(75°) = AB/sin(47°)
Solving for AB, we get:
AB = (230 * sin(47°))/sin(75°)
Using a calculator to compute the sines and perform the multiplication and division, we get:
AB ≈ 172.6 meters
So, Greg and Lucy are approximately 172.6 meters apart from each other.
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