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Question
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
Options
a
2a
3a
None of these
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Solution
We have to find the distance between A(a cos 25°, 0) and B (0 , a cos 65° ) .
In general, the distance between A(x1 , y1 ) and B( x2 ,y2 ) is given by,
`AB = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
So,
\[AB = \sqrt{\left( 0 - a\cos25° \right)^2 + \left( a\cos65° - 0 \right)^2}\]
\[ = \sqrt{\left( a\cos25° \right)^2 + \left( a\cos65° \right)^2}\]
But according to the trigonometric identity,
`sin^2 theta + cos^2 theta = 1`
Therefore,
AB = a
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