KVPY 2013 - 8

Geometry Level 3

{ 2 s i n α + 3 c o s β = 3 2 3 s i n β + 2 c o s α = 1 \large \begin{cases} 2sin\alpha+3cos\beta=3\sqrt{2} \\ 3sin\beta+2cos\alpha=1\end{cases}

The angles α , β , γ \alpha,\beta,\gamma of a triangle satisfy the above given equations.

Then find the angle γ \gamma .

Try the whole set KVPY 2013 SB/SX here.

12 0 ∘ 120^\circ 15 0 ∘ 150^\circ 6 0 ∘ 60^\circ 3 0 ∘ 30^\circ

Skanda Prasad by Skanda Prasad , 20, India

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