The angles of a triangle are in the ratio 3 : 4 : 5, then the smallest angle in degree and the greatest angle in radians is

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$45 °, \frac{5 π}{12}$

$30 °, \frac{12 π}{5}$

$150 °, \frac{5 π}{12}$

$75 °, \frac{3 π}{12}$

answer is D.

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Detailed Solution

$∠ A = 3 x °, ∠ B = 4 x °, ∠ C = 5 x °$

$A + B + C = 180 °$

$3 x + 4 x + 5 x = 180 °$

$12 x = 180 °$

$x = 15 °$

$∴$ Smallest angle = 3x = 3(15°) = 45°

Greatest angle $= 5 x = 5 (15) = 75 °$

$= 75 \times \frac{π}{180} = \frac{5 π}{12}$ radians

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