Answer to Question #296860 in Classical Mechanics for Nixon

Question #296860

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 ?

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Expert's answer
2022-02-13T17:45:16-0500

tanα=hx+a,\tan\alpha=\frac h{x+a}, tanβ=ha,\tan\beta=\frac ha,

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

x=h(1tanα1tanβ)=33.8 ft.x=h(\frac 1{\tan \alpha}-\frac 1{\tan\beta})=33.8~ft.


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