Angles of elevation

From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of the building.

Correct result:

h =  69.73 m
d1 =  165 m
d2 =  116 m

Solution:

a=57 m A=25 rad=25 π180 =25 3.1415926180 =0.43633=5π/36 B=37 rad=37 π180 =37 3.1415926180 =0.64577  tanA=ha+b tanB=hb b=htanB  atanA+btanA=h atanA+htanBtanA=h  h=a tan(A)1tan(A)/tan(B)=57 tan(0.4363)1tan(0.4363)/tan(0.6458)=69.73 m
b=htan(B)=69.728tan(0.6458)92.5322 m  d1=h2+(a+b)2=69.7282+(57+92.5322)2=165 m
d2=h2+b2=69.7282+92.53222=116 m



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