The tower

The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?

Correct answer:

y2 =  37.9832 m

Step-by-step explanation:

h=96 m A=30+10/60=618130.1667  B=20+50/60=612520.8333   h = y1+y2 tan A = y1/x tan B = y2/x  tan A/tan B = y1/y2 tan A/tan B = (hy2)/y2  t=tanA/tanB=tan30.166666666667° /tan20.833333333333° =0.581235/0.38053=1.52744  t = (hy2)/y2 y2 t = hy2  y2(t+1)=h  y2=h/(t+1)=96/(1.5274+1)37.9832 m   Verifying Solution:  y1=hy2=9637.983258.0168 m x=y1/tanA=y1/tan30.166666666667° =58.0168/tan30.166666666667° =58.0168/0.581235=99.816 m

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