Question

The distance between the points $(acos{25}^{\circ },0)$ and $(0,acos{65}^{\circ })$ is ___.

• A. $acos{35}^{\circ }$
• B. $2\sqrt{a}$
• C. $a$
• D. $0.5a$

Answer 1

The correct option is C

$a$

Required distance
$=\sqrt{(acos{25}^{\circ }-0{)}^2+(0-acos{65}^{\circ }{)}^2}=\sqrt{a^{2}co{s}^2{25}^{\circ }+a^{2}co{s}^2{65}^{\circ }}=\sqrt{a^{2}co{s}^2{25}^{\circ }+a^{2}co{s}^2({90}^{\circ }-{25}^{\circ })}=\sqrt{a^{2}co{s}^2{25}^{\circ }+a^{2}si{n}^2{25}^{\circ }}=\sqrt{a^2(co{s}^2{25}^{\circ }+si{n}^2{25}^{\circ })}=\sqrt{a^2\times \left(1\right)}=a$