A particle is thrown over a triangle from one end of a horizontal base and after grazing the vertex falls on the other end of the base. If 30° and 60° be the base angles and θ the angle of projection then tanθ is

Question

A particle is thrown over a triangle from one end of a horizontal base and after grazing the vertex falls on the other end of the base. If 30° and 60° be the base angles and θ the angle of projection then tanθ is (A) (2/√3) (B) (4/√3) (C) (1/3) (D) 3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-erzqby2pplyct9tt.jpg" /> tan θ =tan â¡ α +tan â¡ β tan θ =tan â¡ 30o+tan â¡ 60o tan θ =(1/√3)+√3 tan θ =(4/√3)

Q. A particle is thrown over a triangle from one end of a horizontal base and after grazing the vertex falls on the other end of the base. If $3 0^{\circ}$ and $6 0^{\circ}$ be the base angles and $θ$ the angle of projection then $t an θ$ is

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{1}{3}$

3

$t an θ = t an α + t an β$
$t an θ = t an 3 0^{o} + t an 6 0^{o}$
$t an θ = \frac{1}{3} + 3$
$t an θ = \frac{4}{3}$

Q. A particle is thrown over a triangle from one end of a horizontal base and after grazing the vertex falls on the other end of the base. If 30∘ and 60∘ be the base angles and θ the angle of projection then tanθ is

3​2​

3​4​

31​

3

tanθ=tan⁡α+tan⁡β tanθ=tan⁡30o+tan⁡60o tanθ=3​1​+3​ tanθ=3​4​

Q. A particle is thrown over a triangle from one end of a horizontal base and after grazing the vertex falls on the other end of the base. If $3 0^{\circ}$ and $6 0^{\circ}$ be the base angles and $θ$ the angle of projection then $t an θ$ is

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{1}{3}$

$t an θ = t an α + t an β$
$t an θ = t an 3 0^{o} + t an 6 0^{o}$
$t an θ = \frac{1}{3} + 3$
$t an θ = \frac{4}{3}$