Observation 63194

Determine the height of the cloud above the lake's surface if we see it from place A at an elevation angle of 20° 57'. From the same place A, we see its image in the lake at a depth angle of 24° 12'. Observation point A is 115m above the lake level.

Correct answer:

h =  1438.0998 m

Step-by-step explanation:

α=20+57/60=20419=20.95  β=24+12/60=5121=24.2   y=115 m  tan α = (hy):x tan β = (h+y):x   tan βtan α  =  h+yhy  (h+y)   tan α  = (hy)   tan β  t1=tanα=tan20.95° =0.382863=0.38286 t2=tanβ=tan24.2° =0.449418=0.44942  h t1 + y t1 = h t2  y t2 h(t1t2)  =  y t1  y t2  h=y t2t1t1+t2=115 0.44940.38290.3829+0.4494=1438.0998 m

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