# The angles of a triangle are in the ratio 3 : 4 : 5.Find the smallest angle in degrees and the greatest angle in radians

$\begin{array}{1 1}(a)\;15^{\large\circ}&(b)\;45^{\large\circ},\large\frac{5\pi}{2}\\(c)\;75^{\large\circ},\large\frac{\pi}{2}&(d)\;None\;of\;these\end{array}$

Let the three angles be $3x,4x,5x$ degrees then
$3x+4x+5x=180^{\large\circ}$
$12x=180^{\large\circ}$
$x=\large\frac{180^{\large\circ}}{12}$
$x=15^{\large\circ}$
Smallest angle =$3x$
$\qquad\qquad\quad\;=3\times 15^{\large\circ}$
$\qquad\qquad\quad\;=45^{\large\circ}$
Greatest angle =$5x$
$\qquad\qquad\quad=5\times 15^{\large\circ}$
$\qquad\qquad\quad=75^{\large\circ}$
In radian $\Rightarrow 75^{\large\circ}\times\large\frac{\pi}{180^{\large\circ}}$
$\Rightarrow \large\frac{5\pi}{12}$ radians.
Hence (b) is the correct answer.