Elevation 80866

Find the height of the tower when the geodetic measured two angles of elevation α=34° 30'' and β=41°. The distance between places AB is 14 meters.

Correct answer:

h =  46 m

Step-by-step explanation:

a=14 m α=41°=41 β=34°30=34°+6030°=34.5°=34.5  tan α = h/x tan β = h/(x+a)  x = h / tan α  = h   t1 t1=1/tanα=1/tan41° =1/0.869287=1.15037 t2=tanβ=tan34.5° =0.687281=0.68728  t2 (h t1+a) = h t2 h t1+a t2 = h  h=1t2 t1a t2=10.6873 1.150414 0.687345.9558 m   Verifying Solution:  x=h t1=45.9558 1.150452.8661 m α2=π180°arctan(xh)=π180°arctan(52.866145.9558)=41  β2=π180°arctan(x+ah)=π180°arctan(52.8661+1445.9558)=269=34.5 



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