Question

The distance between the points ($a\cos {55}^{\circ }$, 0) and (0, $a\cos {35}^{\circ }$) is -

• A. a
• B. 2a
• C. 3a
• D. 4a

Answer 1

The correct option is A

a

The distance between ($a\cos {55}^{\circ }$, 0) and (0, $a\cos {35}^{\circ }$) is

$\sqrt{{(a\cos {55}^{\circ }-0)}^2+{(0-a\cos {35}^{\circ })}^2}$

=$\sqrt{a^2{\cos }^2{55}^{\circ }+a^2{\cos }^2{35}^{\circ }}$

=$a\sqrt{{\cos }^2{55}^{\circ }+{\cos }^2{35}^{\circ }}$

We know that $\cos$ 55 = $\sin$ 35

So the distance will be

$a\sqrt{{\sin }^2{35}^{\circ }+{\cos }^2{35}^{\circ }}$

${\sin }^2$x + ${\cos }^2$x = 1

Thus, distance = $a\sqrt{1}$ = a.