Question

From two points each on the opposite sides of a river . The angles of elevation of the top of an 80 feet tree are 60° and 30°. The points and the tree are in the same straight line , which is perpendicular to the river. How wide is the river ?

Answer 1

$\tan\alpha=\frac h{x+a},$ $\tan\beta=\frac ha,$

$x=\frac h{\tan \alpha}-a,$ $a=\frac h{\tan \beta},$

$x=h(\frac 1{\tan \alpha}-\frac 1{\tan\beta})=33.8~ft.$