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