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 ?
tanα=hx+a,\tan\alpha=\frac h{x+a},tanα=x+ah, tanβ=ha,\tan\beta=\frac ha,tanβ=ah,
x=htanα−a,x=\frac h{\tan \alpha}-a,x=tanαh−a, a=htanβ,a=\frac h{\tan \beta},a=tanβh,
x=h(1tanα−1tanβ)=33.8 ft.x=h(\frac 1{\tan \alpha}-\frac 1{\tan\beta})=33.8~ft.x=h(tanα1−tanβ1)=33.8 ft.
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