Trigonometry and Geometry Quiz
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Questions and Answers

If the perimeter and the area of a circle are numerically equal, what is the radius of the circle?

  • 4 units
  • π units (correct)
  • 2 units
  • 7 units

    • In a locality, a single circular park is proposed to be built equal in area to the sum of areas of two circular parks with diameters 16 m and 12 m. What will be the radius of the new park?

  • 20m
  • 15m (correct)
  • 24m
  • 10m

    • Given that sin θ = 1/2√3, what is cos θ?

  • b/√(b^2 - a^2)
  • a/√(b^2 - a^2) (correct)
  • b
  • b/a√(b^2 - a^2)

    • In a right triangle, the length of the hypotenuse is 13 cm and one of the angles is 30 degrees. What is the length of the side opposite the 30-degree angle?

    <p>7$\sqrt{3}$ cm</p> Signup and view all the answers

    If the speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h, what is the time taken to travel 24 km upstream?

    <p>3 hours</p> Signup and view all the answers

    If two water taps can fill a tank in 9 hours together, with the larger tap taking 8 hours less than the smaller tap to fill the tank alone, how long would it take for the smaller tap to fill the tank on its own?

    <p>24 hours</p> Signup and view all the answers

    In a circle with centre O, chord AB makes an angle of 30° with the radius at the point of contact. If the length of the chord is 6 cm, what is the length of the tangent PA?

    <p>3 cm</p> Signup and view all the answers

    If $1 + \sin^2\theta = 3\sin\theta\cos\theta$, what is the value of $\tan\theta$?

    <p>1</p> Signup and view all the answers

    If a motor boat with a speed of 18 km/h in still water takes 1 hour to travel, what is the speed of the stream if it travels in one direction?

    <p>8 km/h</p> Signup and view all the answers

    Given the length-frequency table for leaves, what is the average length of the leaves to the nearest millimeter?

    <p>150 mm</p> Signup and view all the answers

    Study Notes

    Circle Properties

    • If the perimeter and area of a circle are equal, the radius can be determined.
    • The area of a circle is equal to the sum of areas of two smaller circles with diameters 16m and 12m.

    Trigonometry

    • If sin θ = 1/2√3, then cos θ can be calculated.
    • In a right triangle, the length of the hypotenuse and one of the angles can be used to determine the length of the side opposite the angle.

    Motion

    • The speed of a boat in still water and the speed of the stream can be used to determine the time taken to travel upstream.
    • The speed of a motor boat in still water and the time taken to travel can be used to determine the speed of the stream.

    Time and Work

    • If two taps can fill a tank together, and the larger tap takes less time to fill the tank alone, the time taken by the smaller tap to fill the tank alone can be determined.

    Geometry

    • In a circle, the angle of a chord with the radius at the point of contact can be used to determine the length of the tangent.
    • The length of a chord and the angle it makes with the radius can be used to determine the length of the tangent.

    Algebra

    • The equation 1 + sin^2θ = 3sinθcosθ can be solved to determine the value of tanθ.

    Statistics

    • A length-frequency table for leaves can be used to determine the average length of the leaves to the nearest millimeter.

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    Description

    Test your knowledge on trigonometry and geometry concepts with this quiz. Questions involve calculations for sine, cosine, shadow lengths, circle properties, and more.

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