Question

The sum of two angles is 3 radians and their difference is 40 degrees. Find the angles in radian.

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Sum of two angles is 3 radians and}$

$\mathsf{their\;difference\;is\;40^{\circ}}$

$\underline{\textsf{To find:}}$

$\textsf{The angles in radians}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the two angles be A and B}$

$\mathsf{First\;we\;convert\;40^{\circ}\;into\;radians}$

$\mathsf{40^{\circ}=40{\times}\dfrac{\pi}{180}\,radians=\dfrac{2\pi}{9}\,radians}$

$\textsf{As per given data,}$

$\mathsf{A+B=3}$

$\mathsf{A-B=\dfrac{2\pi}{9}}$

$\mathsf{Adding\;the\;equations,we\;get}$

$\mathsf{2A=3+\dfrac{2\pi}{9}}$

$\mathsf{2A=\dfrac{27+2\pi}{9}}$

$\implies\boxed{\mathsf{A=\dfrac{27+2\pi}{18}}}$

$\mathsf{A+B=3}$

$\implies\mathsf{\dfrac{27+2\pi}{18}+B=3}$

$\implies\mathsf{B=3-\left(\dfrac{27+2\pi}{18}\right)}$

$\implies\mathsf{B=\dfrac{54-27-2\pi}{18}}$

$\implies\boxed{\mathsf{B=\dfrac{27-2\pi}{18}}}$

$\underline{\textsf{Answer:}}$

$\mathsf{A=\dfrac{27+2\pi}{18}\;radians}$

$\mathsf{B=\dfrac{27-2\pi}{18}\;radians}$