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A particle thrown over a triangle from one end of a horizontal base falls on the other end of the base after grazing the vertex. If `alpha and beta` are the base angles of triangle and angle of projection is `theta`, then prove that `( tan theta = tan alpha + tan beta)`

Text Solution

Verified by Experts

From triangle `y=x tan alpha`
`y=(R-x)tan beta`
` because y=x tan theta[1-(x)/(R)]rArr tan theta=(yR)/(x(R-x)) therefore tan theta=tan alpha+tan beta` (H.P)
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Knowledge Check

  • A particle is thrown over a triangle from one end of horizontal base and grazing over the vertex falls on the other end of the base. If alpha, beta are the base angles and theta the angle of projection, then

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    D
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