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    Please can someone explain why the angle is tan(60)? Why did they choose the tangent function? I understand the other steps involved in answering the Q.
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    (Original post by Whosthat?)
    Please can someone explain why the angle is tan(60)? Why did they choose the tangent function? I understand the other steps involved in answering the Q.
    Uh, the angle is 60^{\circ}, not \tan 60^{\circ}. Presumably the tangent function was the easier one to work with but you could have just as well chosen the sine or cosine.
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    (Original post by Zacken)
    Uh, the angle is 60^{\circ}, not \tan 60^{\circ}. Presumably the tangent function was the easier one to work with but you could have just as well chosen the sine or cosine.
    But there must be a reason why they chose tan(60). How did they know which function is the correct one to use? Because I couldn't use cos(60) or sin(60) and get the correct answer.

    I've attached the mark scheme.
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    (Original post by Whosthat?)
    But there must be a reason why they chose tan(60). How did they know which function is the correct one to use? Because I couldn't use cos(60) or sin(60) and get the correct answer.

    I've attached the mark scheme.
    They've used \tan 30^{\circ} - i.e: they constructed a right angle triangle by bisecting the angle. We want to use the tangent function because that gives us information about the adjacent and opposite - which is all we have and want. The hypotenuse is of no use to us.

    We know that V = \frac{1}{3} \pi r^2 h but we want this in terms of only h so lo-and-behold, we need to find a way of writing r as a function of h - using the tangent gives us \tan 30^{\circ} = \frac{r}{h} allowing us to write r as a multiple of h which can then be substituted into the formula for volume to turn it into a formula that involves just h.
 
 
 
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