Question

Find the distance between the points $(a\cos {60}^{\circ },0)$ and $(0,a\sin {60}^{\circ },0)$

• A. $a$ units
• B. $\frac{a}{4}$ units
• C. $\frac{a}{2}$ units
• D. $\frac{a}{3}$ units

Answer 1

The correct option is A $a$ units

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula:

$\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Distance between the points $(a\cos {60}^0,0)$ and $(0,a\sin {60}^0)$

$=\sqrt{{(0-a\cos {60}^0)}^2+{\left(a\sin {60}^0\right)}^2}=\sqrt{{(-\frac{a}{2})}^2+{(-\frac{\sqrt{3}a}{2})}^2}=\sqrt{\frac{{4a}^2}{4}}=a$