Angle of Elevation

Please help to solve this problem:
The angle of elevation of a point C from a point B is 29042'; the angle of elevation of C from another point A 31.2 m directly below B is 59023'. How high is C from the horizontal line through A?

α=905923=3037

β=90+2942=11942

θ=180αβ=2941
 

trigo_001_angle-of-elevation.gif

 

xsinβ=31.2sinθ

x=54.73 m
 

y=xsin5923

y=47.098 m       answer

img_20170418_162702.jpg

AB=A'B'=31.2m
AA'=BB'=X
A'C=y=31.2 + y'
y=31.2 + y'

tan 29042'=y'/x

x = y'/ tan 29042'
tan 59023'=y/x
tan 59023'=(31.2+y')/(y'/(tan 29042')
(tan 59023')(y')/(tan29042')=31.2 +y'
2.9625y'-y'=31.2
y'=31.2/1.9625
y'=15.898m
y=31.2 + 15.898
y=47.098m Ans