Question

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

• A. a
• B. 2a
• C. 3a
• D. 4a

Answer 1

The correct option is A

a

$\cos$ 35 = $\sin$ 65
Applying distance formula we get

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

$\Rightarrow \sqrt{{\text{a}}^{2}co{s}^2{35}^{\circ }+{\text{a}}^{2}co{s}^2{55}^{\circ }}$

$\Rightarrow \sqrt{{\text{a}}^2(co{s}^2{35}^{\circ }+co{s}^2{55}^{\circ })}$

Since cos 55 = sin 35 and ${\sin }^2$x + ${\cos }^2$x = 1
$\Rightarrow \sqrt{a^2}=a$