Expert: Richard J. Raridon - 3/17/2005

Question
1) how many different triangles PQR can be constructed using the given information?
a. p=5, q=4, angle Q=74 degrees
b. p=9, q=8, angle P=23 degrees

2) observers at points A and B, 30 km apart, sight an airplane at angles of elevation of 40 degrees and 75 degrees, respectively. how far is the plane from each observer?

Answer
1)a. can't do it.  4/sin(74) = 5/sin(P) and sin(P) > 1
b. Q = 20.3 degrees and 3rd angle = 136.7 degrees
2) First, find the height h of the plane.  Let x = horizontal distance from B to the plane
tan(40) = h/(30+x) and tan(75) = h/x so h = 32.5 km
Distance from A to plane = R where sin(40) = h/R so R = 50.5 km
Distance from B to plane = R where sin(75) = h/R so R = 33.6 km