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Math Help - Trigonometric differentiation problem

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    Trigonometric differentiation problem

    1.The base of an isosceles triangle is 20cm and the altitude is increasing at the rate of 1cm/min. At what rate is the base angle increasing when the area is 100cm^2?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by matthewspj View Post
    1.The base of an isosceles triangle is 20cm and the altitude is increasing at the rate of 1cm/min. At what rate is the base angle increasing when the area is 100cm^2?
    A is the area, h is the height, b is the length of the base and \theta is the base angle.

    recall that A = \frac 12 bh

    this means, when A = 100, h = 10.

    we are also told that \frac {dh}{dt} = 1. b is constant at 20cm, and so \frac {db}{dt} = 0, but we wont even have to worry about that.

    draw your triangle, and bisect the base with a vertical line going through the top vertice. \theta is the base angle and we form a right triangle with the opposite side to theta being h and the adjacent side being 10.

    Thus we have \sin \theta = \frac h{10}

    now differentiate implicitly and continue
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