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in Mathematics by (44.4k points)
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The distance between the points \((5\cos \theta, 0)\) and \((0, 5\sin\theta)\) is

(A) 10

(B) 5

(C) 30

(D) 25

1 Answer

+1 vote
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Best answer

Correct option is (B) 5

Given the point \(A=(5 \cos \theta, 0)\) and \(B=(0,5 \sin \theta)\)

By distance formula,

The distance of \(A B =\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\)

\(=\sqrt{(0-5 \cos \theta)^{2}+(5 \sin \theta-0)^{2}}\)

\(=\sqrt{(-5 \cos \theta)^{2}+(5 \sin \theta)^{2}} \)

\(=\sqrt{25 \cos ^{2} \theta+25 \sin ^{2} \theta}\)

\(=\sqrt{25\left(\sin ^{2} \theta+\cos ^{2} \theta\right)}\)

\(=\sqrt{25 \times 1}\)

\(=5\)

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