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^circ -  0)^2 + (0 - 5  sin 30^circ)^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^circ + cos^2 60^circ) `

= 5