Random Angle II - QuantGuide

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Random Angle II

Easy

Probability

A right triangle is being formed with legs labeled

A

and

B

. The random lengths of legs

A

and

B

are both IID Unif

(0,1)

RVs. Let

\theta

be the angle (of random degree measure) that is opposite of side

A

. Find the probability

\theta > \dfrac{\pi}{3}

. The answer is in the form

\dfrac{a}{b\sqrt{c}}

for integers

a,b,c

that are relatively prime. Find

abc

Notes

Hint

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Random Angle II

Easy

Probability

A right triangle is being formed with legs labeled

A

and

B

. The random lengths of legs

A

and

B

are both IID Unif

(0,1)

RVs. Let

\theta

be the angle (of random degree measure) that is opposite of side

A

. Find the probability

\theta > \dfrac{\pi}{3}

. The answer is in the form

\dfrac{a}{b\sqrt{c}}

for integers

a,b,c

that are relatively prime. Find

abc

Notes

Hint