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In right-angled triangle,the difference between the two acute angles is $(\large\frac{\pi}{15})^c$.Find the angles in degrees

$\begin{array}{1 1}(A)\;51^{\large\circ},39^{\large\circ},90^{\large\circ}\\(B)\;50^{\large\circ},40^{\large\circ},95^{\large\circ}\\(C)\;60^{\large\circ},40^{\large\circ},70^{\large\circ}\\(D)\;80^{\large\circ},50^{\large\circ},90^{\large\circ}\end{array} $

1 Answer

Toolbox:
  • Degree measure =$\large\frac{180}{\pi}$$\times$ radian measure
The sum of the two acute angles of a right triangle is $90^{\large\circ}$
Difference between the actute angles
$\large\frac{\pi}{15}^c=(\frac{\pi}{15}\times \frac{180}{\pi})^{\large\circ}$
$\Rightarrow 12^{\large\circ}$
Let the two acute angles be $x^{\large\circ}$ and $y^{\large\circ}$ then,
$x+y=90^{\large\circ}$--------(1)
$x-y=12^{\large\circ}$--------(2)
____________________
$2x=102^{\large\circ}$
$x=51^{\large\circ}$
$\Rightarrow y=39^{\large\circ}$
Hence the angles of a triangle are $51^{\large\circ},39^{\large\circ},90^{\large\circ}$
Hence (A) is the correct answer.
answered May 21, 2014 by sreemathi.v
 

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