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 answer:

h =  69.73 m
d1 =  165 m
d2 =  116 m

Step-by-step explanation:

a=57 m A=25° rad=25° 180π =25° 1803.1415926 =0.43633=5π/36 B=37° rad=37° 180π =37° 1803.1415926 =0.64577  tan A = a+bh tan B = bh b = tan Bh  a tan A + b tan A = h a tan A +  tan Bh tan A = h  h=1tan(A)/tan(B)a tan(A)=1tan0.4363/tan0.645857 tan0.4363=69.73 m
b=tan(B)h=tan0.645869.72892.5322 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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