Applications in Trigonometry2

1. A balloon B is observed simultaneously from two points P and Q on a horizontal ground. P is at a distance of c metres due north of Q. R is the projection of B on the ground. The bearings of the balloon from P and Q are SαﾟE and NβﾟE respectively. The angle of elevation of B from P is θﾟ.

(a) If the height of the balloon is h meters, show that
h = (ctanθﾟsinβﾟ) / [sin(αﾟ + βﾟ)].
(b) Given thatθ = 40, α = 54 and β = 46, find
(i) h / c,
(ii) the angle of elevation of B from Q,
(iii) the angle of elevation and the bearing of B from M, where M is the mid-point of PQ.

http://i617.photobucket.com/albums/tt257/michaelcoco_/2.jpg

※ 只需計算(b)(iii)※

The answer of (b)(iii) is:
Angle of elevation = 45.8ﾟ, bearing = N83.2ﾟE