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A particle is projected over a triangle...

A particle is projected over a triangle from one end of a horizontal base and garzing the vertex falls on the other end of the base . If `alpha` and `beta` the base angles and `theta` the angle of projection then show that ` tan theta = tan alpha + tan beta`.

Answer

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Explore conceptually related problems

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

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

Knowledge Check

  • If alpha, beta are the solutions of a cos 2theta + b sin 2theta = c , then tan alpha tan beta=

    A
    `(c+a)/(c-a)`
    B
    `(2b)/(c+b)`
    C
    `(c-a)/(c+a)`
    D
    none

  • If alpha and beta are angles in the first quadrant sucn than tan alpha = 1/7 and sin beta = (1)/(sqrt10) , then alpha + 2 beta =

    A
    `30^@`
    B
    `45^@`
    C
    `75^@`
    D
    `90^@`

  • If alpha, beta are solutions of a tan theta + b sec theta = c then tan (alpha + beta)=

    A
    `(2ac)/(a^(2)-c^(2))`
    B
    `(2ac)/(c^(2)-a^(2))`
    C
    `(2ac)/(a^(2)+c^(2))`
    D
    none

    • Similar Questions

    Explore conceptually related problems

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

    A particle is thrown over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. If alpha and beta be the base angles and theta be the angle of projection, prove thattam theta=tanalpha+tanbeta .

    Two particles are projected at the same instant from the same point at inclinations alpha and beta to the horizontal. If they simultaneously hit the top and bottom of a vertical pole subtending angle theta at the point of projection , find (tan alpha - tan beta) .

    If theta is the angle of projection, R the range, h the maximum height. T the time of flight then show that (a) tan theta = 4h//R and (b) h = g T^(2//8) .

    If theta is the angle of projection, R the range, h the maximum height , T the time of flight , then show that (a) tan theta = 4h / R and (b) h = gT^(2)// 8

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