Q71 / 160 · TS EAMCET 2006 · Mathematics

The angles of a triangle are in the ratio $3: 5: 10$. Then the ratio of the smallest side to the greatest side is :

  • A
    $1: \sin 10^{\circ}$
  • B
    $1: 2 \sin 10^{\circ}$
  • C
    $1: \cos 10^{\circ}$
  • Correct answer
    D
    $1: 2 \cos 10^{\circ}$

Solution

Let the angles of a triangle are $3 x, 5 x$ and $10 x$. $\therefore \quad 3 x+5 x+10 x=180^{\circ}$ $\Rightarrow \quad x=10^{\circ}$ $\therefore$ Smallest angle of a triangle $=30^{\circ}$ and the greatest angle $=100^{\circ}$ Required ratio $=\sin 30^{\circ}: \sin 100^{\circ}$ $=\frac{1}{2}: \cos 10^{\circ}$ $=1: 2 \cos 10^{\circ}$

Hence, the correct answer is option: 'D'.

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