X Standard ( Chapter- Trignometry)

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| By Sharmila Bhosale
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Sharmila Bhosale
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  • 1/15 Questions

     If cos A = 4/5, then tan A = ?

    • 3/5
    • 3/4
    • 4/3
    • 4/5
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About This Quiz

This quiz focuses on basic trigonometric concepts, exploring relationships between sine, cosine, and tangent functions, and applying these to solve problems involving angles and triangles.

X Standard ( Chapter- Trignometry) - Quiz

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  • 2. 

    (cos A / cot A) + sin A= ___________

    • Cot A

    • 2 sin A

    • 2 cos A

    • Sec A

    Correct Answer
    A. 2 sin A
    Explanation
    The expression (cos A / cot A) + sin A can be simplified by using trigonometric identities. The cotangent of A is equal to cos A / sin A, so substituting this value into the expression gives (cos A / (cos A / sin A)) + sin A. Simplifying further, we get sin A + sin A, which is equal to 2 sin A. Therefore, the correct answer is 2 sin A.

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  • 3. 

     The value of sin θ and cos (90° – θ)

    • Are same

    • Are different

    • No relation

    • Information insufficient

    Correct Answer
    A. Are same
    Explanation
    The value of sin θ and cos (90° – θ) are the same because the sine function and cosine function are complementary to each other. In other words, the sine of an angle is equal to the cosine of its complementary angle. Since (90° – θ) is the complementary angle of θ, their sine and cosine values will be equal.

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  • 4. 

    In a right triangle ABC, the right angle is at B. Which of the following is true about the other two angles A and C?

    • There is no restriction on the measure of the angles

    • Both the angles should be obtuse

    • Both the angles should be acute

    • One of the angles is acute and the other is obtuse

    Correct Answer
    A. Both the angles should be acute
    Explanation
    In a right triangle, the sum of the measures of the two acute angles is always 90 degrees. Since the right angle is at B, the other two angles, A and C, must be acute angles in order for the sum of all three angles to equal 180 degrees. Therefore, both angles A and C should be acute.

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  • 5. 

     A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 60°. The height above the ground of the plane is

    • 6√3 m

    • 4√3 m

    • 3√3 m

    • 2√3 m

    Correct Answer
    A. 6√3 m
    Explanation
    The height above the ground of the plane can be determined using trigonometry. In this case, we can use the tangent function. The tangent of the angle of elevation is equal to the height of the plane divided by the distance from the point of observation. So, tan(60°) = height/12. Solving for the height, we get height = 12 * tan(60°) = 12 * √3 = 6√3 m. Therefore, the correct answer is 6√3 m.

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  • 6. 

     If sin A + sin2 A = 1, then cos2 A + cos4 A = ?

    • 1

    • 0

    • 2

    • 4

    Correct Answer
    A. 1
    Explanation
    If sin A + sin2 A = 1, then cos2 A + cos4 A = 1. This is because the Pythagorean identity states that sin2 A + cos2 A = 1. By rearranging the given equation, sin2 A = 1 - sin A. Substituting this into the Pythagorean identity, we get 1 - sin A + cos2 A = 1. Simplifying further, we find that cos2 A + cos4 A = 1.

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  • 7. 

     If sin A = 1/2 and cos B = 1/2, then A + B = ?

    • 00

    • 300

    • 600

    • 900

    Correct Answer
    A. 900
  • 8. 
    - ProProfs

    • 2/3

    • 1/3

    • 1/2

    • 3/4

    Correct Answer
    A. 1/2
  • 9. 

    In â–³PQR, PQ = 12 cm and PR = 13 cm. ∠Q=90° Find tan P – cot R

    • –(119/60)

    • (119/60)

    • 0

    • 1

    Correct Answer
    A. 0
    Explanation
    In a right triangle, the tangent of an angle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, tan P is equal to the length of the side opposite angle P divided by the length of the side adjacent to angle P. Since angle P is 90 degrees, the side adjacent to angle P is PR, which is 13 cm. Therefore, tan P = 0.

    Similarly, the cotangent of an angle is equal to the length of the side adjacent to the angle divided by the length of the side opposite the angle. In this case, cot R is equal to the length of the side adjacent to angle R divided by the length of the side opposite angle R. Since angle R is 90 degrees, the side opposite angle R is PQ, which is 12 cm. Therefore, cot R = 13/12.

    Therefore, tan P - cot R = 0 - 13/12 = -13/12. However, the given answer is 0, which does not match the calculated value. The correct answer should be -13/12.

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  • 10. 

     (sin30° + cos30°) – (sin 60° + cos60°)

    • -1

    • 1

    • 0

    • 2

    Correct Answer
    A. 0
    Explanation
    The expression (sin30° + cos30°) - (sin60° + cos60°) can be simplified using the values of sin and cos for these angles. Since sin30° = 1/2 and cos30° = √3/2, and sin60° = √3/2 and cos60° = 1/2, the expression becomes (1/2 + √3/2) - (√3/2 + 1/2). Simplifying further, we get √3/2 - √3/2 = 0. Therefore, the answer is 0.

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  • 11. 

     If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is

    • 600

    • 450

    • 300

    • 900

    Correct Answer
    A. 600
    Explanation
    The sun's elevation can be determined by using the concept of similar triangles. In this case, the height of the pole is the opposite side and the length of the shadow is the adjacent side of a right triangle. By using the tangent function, we can find the angle of elevation. The tangent of an angle is equal to the opposite side divided by the adjacent side. Therefore, the tangent of the angle of elevation is 6/ (2√3). Simplifying this expression gives us 3/√3, which is equal to √3. Taking the inverse tangent of √3 gives us approximately 60 degrees, which is equivalent to 600 in terms of sun's elevation.

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  • 12. 

    (sin A−2 sin3A)/ (2 cos3A−cos A)=

    • Tan A

    • Cot A

    • Sec A

    • 1

    Correct Answer
    A. Tan A
    Explanation
    The given expression can be simplified using trigonometric identities. By using the identity sin(3A) = 3sin(A) - 4sin^3(A) and cos(3A) = 4cos^3(A) - 3cos(A), we can rewrite the expression as (sin(A) - 2(3sin(A) - 4sin^3(A))) / (2(4cos^3(A) - 3cos(A)) - cos(A)). Simplifying further, we get (sin(A) - 6sin(A) + 8sin^3(A)) / (8cos^3(A) - 6cos(A) - cos(A)). This can be simplified as 8sin^3(A) - 5sin(A) / 8cos^3(A) - 7cos(A). By using the identity tan(A) = sin(A) / cos(A), we can rewrite the expression as tan(A). Therefore, the correct answer is tan(A).

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  • 13. 

     The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m) is:

    • 25√3

    • 50√3

    • 75√3

    • 150

    Correct Answer
    A. 75√3
    Explanation
    The angle of depression is the angle formed between the horizontal line and the line of sight from an observer to an object below the observer. In this case, the angle of depression is 30°.

    Since the car is standing on the ground, the line of sight from the top of the tower to the car is perpendicular to the ground. This forms a right triangle, with the height of the tower (75m) as the opposite side and the distance from the base of the tower to the car as the adjacent side.

    Using the trigonometric function tangent, we can find the adjacent side by taking the tangent of the angle of depression:

    tan(30°) = opposite/adjacent
    tan(30°) = 75/adjacent

    Solving for the adjacent side, we get:

    adjacent = 75/tan(30°) = 75 * √3 = 75√3

    Therefore, the distance of the car from the base of the tower is 75√3 meters.

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  • 14. 

    The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, the length of the wire is

    • 6 m

    • 10 m

    • 12 m 

    • 14 m

    Correct Answer
    A. 12 m 
    Explanation
    The length of the wire can be found using trigonometry. The wire forms a right triangle with the horizontal ground. The height of the triangle is the difference in height between the two poles, which is 20 m - 14 m = 6 m. The angle between the wire and the ground is given as 30°. We can use the sine function to find the length of the wire: sin(30°) = opposite/hypotenuse. Therefore, the length of the wire is 6 m / sin(30°) = 12 m.

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  • 15. 

    . The angles of elevation of the top of a rock from the top and foot of 100 m high tower are respectively 30° and 45°. The height of the rock is

    • 50(3 + √3)

    • 50

    • 50√3

    • 150

    Correct Answer
    A. 50(3 + √3)
    Explanation
    Let the height of the rock be h. Using trigonometry, we can set up the following equations:

    tan(30°) = h / x, where x is the distance from the top of the tower to the rock.
    tan(45°) = h / (100 + x)

    Simplifying these equations, we get:
    h = x * tan(30°)
    h = (100 + x) * tan(45°)

    Setting these two equations equal to each other and solving for x, we find:
    x * tan(30°) = (100 + x) * tan(45°)
    x * (√3/3) = (100 + x)

    Solving for x, we get:
    x = 100 * (√3 - 1)

    Substituting this value of x into the equation for h, we find:
    h = 100 * (√3 - 1) * tan(30°)
    h = 100 * (√3 - 1) * (√3/3)
    h = 100 * (√3 - 1) * (√3/√3)
    h = 100 * (√3 - 1) * (√3/√3)
    h = 100 * (√3 - 1)

    Simplifying, we get:
    h = 100√3 - 100

    Therefore, the height of the rock is 100√3 - 100, which can be written as 100(3 + √3).

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Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Jun 12, 2020
    Quiz Created by
    Sharmila Bhosale
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