Question

What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?

 

Answer 1

We have to find the distance between A(5 sin 60° , 0) and B ( 0,5 sin 30° ) .

In general, the distance between A`(x_1 , y_1)`  and B`(x_2 ,y_2)` is given by,

`AB = sqrt((x_2 - x_1 )^2 + (y_2 - y_1)^2)`

So,

`AB = sqrt((5 sin 60° - 0)^2 + (0- 5 sin 30°)^2)`

But according to the trigonometric identity,

`sin^2 theta + cos^2 theta = 1`

And,

`sin 30° = cos 60°`

Therefore,

`AB = sqrt( 5^2 ( sin^2 60° + cos^2 60°) `

       = 5