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An airplane is sighted at the same time by two ground observers who are 3 miles apart and in front of the airp?
An airplane is sighted at the same time by two ground observers who are 3 miles apart and in front of the airplane. They report that the angles of elevation are 15 degrees and 21degrees. How high is the airplane?
By your information, a scalene triangle ABC can be made with angle A = 15, B = 180-21 = 159 and C, where the plane is, = 6. If one extends the triangle to form a right-angled triangle that makes a vertical line from C to the ground (the line AB), one gets another triangle BCD, where B is the 21 degrees, the right angle is 90 degrees and the second C will then be 69 degrees, making the whole of C 75 degrees. we need to find CD for the height of the plane. first, we need to find line BC in the first triangle:
BC/sinA = AB/sinC
BC/sin15 = 3/sin6
BC = 3sin15/sin6
BC = 7,43 miles.
BC is the hypotenuse of the smaller triangle BCD, and we know B = 21 degrees for that triangle, so
sin21 = CD/BC (opposite / hypotenuse)
sin21 = CD/7.43
7.43 * sin21 = CD
CD = 2.66 miles.