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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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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)\;45^{\large\circ},\large\frac{5\pi}{12}\normalsize radians\\(B)\;60^{\large\circ},\large\frac{4\pi}{10}\normalsize radians\\(C)\;75^{\large\circ},\large\frac{5\pi}{12}\normalsize radians\\(D)\;60^{\large\circ},\large\frac{7\pi}{12}\normalsize radians\end{array} $

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1 Answer

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Let the three angles be $3x+4x+5x$ degree
$3x+4x+5x=180^{\large\circ}$
$x=\large\frac{180}{12}$
$x=15^{\large\circ}$
Smallest angle =$3x$
$\Rightarrow 3\times 15$
$\Rightarrow 45^{\large\circ}$
Greatest angle =$5x$
$\Rightarrow 5\times 15$
$\Rightarrow 75^{\large\circ}$
Radian measure =$\large\frac{\pi}{180^{\large\circ}}\times $ degree measure
Radian measure =$\large\frac{\pi}{180^{\large\circ}}$$\times 75$
$\Rightarrow \large\frac{5\pi}{12}$ radians
Hence (A) is the correct answer.
answered May 20, 2014 by sreemathi.v
 

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