The angles of a triangle are in the ratio $3: 5: 10$. Then the ratio of the smallest side to the greatest…
The angles of a triangle are in the ratio $3: 5: 10$. Then the ratio of the smallest side to the greatest side is :
$1: \sin 10^{\circ}$
$1: 2 \sin 10^{\circ}$
$1: \cos 10^{\circ}$
$1: 2 \cos 10^{\circ}$
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 $=\sin 30^{\circ}: \sin 100^{\circ}$
$=\frac{1}{2}: \cos 10^{\circ}$
$=1: 2 \cos 10^{\circ}$