Question

The values of $x$ and $y$ which make the following solutions true are $\cos x^{\circ }=\sin {52}^{\circ }$ and $\cos y^{\circ }=\sin (y^{\circ }+10)$

• A. $x={52}^{\circ },y={30}^{\circ }$
• B. $x={38}^{\circ },y={40}^{\circ }$
• C. $x={48}^{\circ },y={52}^{\circ }$
• D. $x={40}^{\circ },y={50}^{\circ }$

Answer 1

The correct option is B $x={38}^{\circ },y={40}^{\circ }$

$\sin {52}^0=\cos \left(x\right)$
$\sin {52}^0=\sin ({90}^0-x)$
${52}^0={90}^0-x$
$x={90}^0-{52}^0$
$x={38}^0$
Similarly
$\cos y=\sin (y+{10}^0)$
$\sin ({90}^0-y)=\sin (y+{10}^0)$
${90}^0-y=y+{10}^0$
${80}^0=2y$
$y={40}^0$