Question

What are the coordinates of A?

Answer 1

Given,

The measure of angle with pruple is 60 degree.

As known that,

The trigonometric ratio of cos is,

`\begin{gathered} \cos \text{ C=}\frac{\text{side adjacent to angle C}}{\text{ Hypotenuse}} \\ \cos \text{ }60^(\circ)\text{=}\frac{\text{Base}}{\text{ l}} \\ (1)/(2)=\frac{\text{Base}}{\text{ l}} \\ \text{Base}=(1)/(2)\text{ l}\ldots\ldots\ldots\ldots\ldots\ldots.(i) \end{gathered}`

The trigonometric ratio of sin is,

`\begin{gathered} \sin \text{ C=}\frac{\text{side opposite to angle C}}{\text{ Hypotenuse}} \\ \sin \text{ }60^(\circ)\text{=}\frac{\text{perpendicular}}{\text{ l}} \\ \frac{\sqrt[]{3}}{2}=\frac{\text{perpendicular}}{\text{ l}} \\ \text{perpendicular}=\sqrt[]{(3)/(2)\text{ }}\text{l}\ldots\ldots\ldots\ldots\ldots\ldots.(ii) \end{gathered}`

The coordinates of A is (x,y).

The coordinates of A is,

`A=((1)/(2)l,\frac{\sqrt[]{3}}{2}l)`

Hence, the coordiantes of the point A is (1/2l, Sqrt(3)/2l).