Question

Two points R and S are on level ground 350m apart. The bearing of S from R is 147°. From R, the bearing of a radio mast is 055°, and from S, the bearing is 032°. The angle of elevation of the top of the mast from R is 20°. Find the height of the mast
Draw a diagram. Let
M = base of mast
T = top of mast
In ∆RSM, the angles are
R=85°, S=72°, so M=23°
using the law of sines,
s/sinS = m/simM. That is,
RM/sin72° = 350/sin23°
RM = 851.91
To find the mast's height MT, then, solve
MT/RM = tan20°

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