Question #106703
From point A, 100m due south of a tower, the angle of elevation of the top of the tower is 40 degrees. From point B due east of the tower, the angle of elevation of the top of the tower is 20 degrees. How far apart are points A and B?
1
Expert's answer
2020-03-27T17:46:52-0400

OC=OAtan400OC=OA\tan40^0 ,OB=OCtan200OB=\frac{OC}{\tan20^0} , AB=OA2+OB2=OA1+tan2400tan2200252mAB=\sqrt {OA^2+OB^2}=OA\sqrt{1+\frac{\tan^240^0}{\tan^220^0}}\approx252m

if OA=100mOA=100m

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