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Math Help - Basic Trig Ratios - Circles, Tangents and Triangles

  1. #1
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    Exclamation Basic Trig Ratios - Circles, Tangents and Triangles

    --- A sphere of radius 8 cm rests inside a conical funnel whose axis is vertical. The highest point of the sphere is 44 cm above the vertex of the cone. Determine the angle of the cone, correct to one decimal.
    (Answer: 25.7 degrees)

    --- a.) Two tangents from a point A are drawn to a circle with centre C and radius 12cm. If the tangents make an angle of 43 degrees with each other at A, then find the length of each tangent, correct to one decimal.
    b.) Determine the the area of quadrilateral ABCD where B and D are the points of contact of the tangents with the circle. {This part is continuation to part (a) only.}

    I would really appreciate full solutions.
    Thanks!
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  2. #2
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    Quote Originally Posted by rishabhsach View Post
    --- A sphere of radius 8 cm rests inside a conical funnel whose axis is vertical. The highest point of the sphere is 44 cm above the vertex of the cone. Determine the angle of the cone, correct to one decimal.
    (Answer: 25.7 degrees)

    make a sketch and look for a right triangle (it's there) ... you'll be using the inverse sine function to find half the vertex angle of the cone.

    --- a.) Two tangents from a point A are drawn to a circle with centre C and radius 12cm. If the tangents make an angle of 43 degrees with each other at A, then find the length of each tangent, correct to one decimal.
    b.) Determine the the area of quadrilateral ABCD where B and D are the points of contact of the tangents with the circle. {This part is continuation to part (a) only.}

    make a sketch ... right triangles are involved again.
    ...
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  3. #3
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    I ACTUALLY don't get it... Can you please help me with a bit of the solution? I have been on this for an hour! I have a test 2 days from now. I need this solution.
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  4. #4
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    like I said ... make a sketch.

    \angle{BCA} = \arcsin\left(\dfrac{AB}{BC}\right)

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