Assume two radar stations that are 25 miles apart are both tracking a plane. At a given moment, the angle between station 1 and he plan is 73 degrees, while the angle between station 2 and the plane is 46 degrees. With this information, how far is the plan from station 2?

Question

cutiecomittee123 · Answer

I assume we have to find the missing angle first

cutiecomittee123 · Answer

so 180-46-73= 61

blacksteel · Answer

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This is a diagram of the given information. Clearly, we are given two angles and the length of the side between them, so we can use the Angle-Side-Angle formula to solve this problem.

First, we find the third angle in the triangle. Since the sum of the three angles is 180 degrees, the third angle is 180 - 73 - 46 = 61

The Law of Sines tells us that a/sinA = b/sinB = c/sinC, where A, B, and C are the triangle's three angles and a, b, and c are the lengths of the sides opposite each angle. We know the distance between the stations and the angle opposite that side. We want to find the distance from the plane to station 2; if we look at our diagram, this is the side opposite the 73 degree angle. So we get
25/sin(61) = x/sin(73) => x = 25 * sin(73)/sin(61) = 27.33487

cutiecomittee123 · Answer

I think you may have calculted wrong, I got 27.33 for the side oppsite of 73 and 20.50 for the side opposite of 46

cutiecomittee123 · Answer

oh nevermind I read your response wrong. Thanks! lol