Answer to Question #106703 in Trigonometry for Charles

Question

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?

Answer 1

$OC=OA\tan40^0$ ,$OB=\frac{OC}{\tan20^0}$ , $AB=\sqrt {OA^2+OB^2}=OA\sqrt{1+\frac{\tan^240^0}{\tan^220^0}}\approx252m$

if $OA=100m$