Some Applications of Trigonometry Important Questions.

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1. Q1Medium

   What is the angle of elevation when the observer looks at an object above the horizontal level?

   • A.Angle of Depression
   • B.Angle of Elevation
   • C.Angle of Inclination
   • D.Angle of Projection
   Answer: Angle of Elevation

   Explanation: The angle of elevation is formed when the observer looks up at an object that is above the horizontal level. This angle is crucial for calculating heights using trigonometric ratios.

2. Q2Medium

   Which trigonometric ratio is used to find the height of an object when the angle of elevation is known?

   • A.Sine (sin)
   • B.Cosine (cos)
   • C.Tangent (tan)
   • D.Cotangent (cot)
   Answer: Tangent (tan)

   Explanation: The tangent ratio relates the height of the object to the distance from the observer. It is defined as the opposite side over the adjacent side in a right triangle.

3. Q3Medium

   In a right triangle, if the angle of elevation is 45°, what is the relationship between the opposite and adjacent sides?

   • A.Opposite is greater
   • B.Adjacent is greater
   • C.They are equal
   • D.Cannot be determined
   Answer: They are equal

   Explanation: At an angle of 45°, the tangent ratio equals 1, meaning the opposite side (height) is equal to the adjacent side (distance). This property is unique to 45° angles in right triangles.

4. Q4Medium

   What is the angle of depression when an observer looks down at an object below the horizontal level?

   • A.Angle of Elevation
   • B.Angle of Depression
   • C.Angle of Inclination
   • D.Angle of Projection
   Answer: Angle of Depression

   Explanation: The angle of depression is formed when the observer looks down at an object that is below the horizontal level. This angle is essential for calculating distances to objects below the observer's line of sight.

5. Q5Medium

   When calculating the height of a building using trigonometry, which angle is typically used?

   • A.Angle of Depression
   • B.Angle of Elevation
   • C.Angle of Inclination
   • D.Angle of Projection
   Answer: Angle of Elevation

   Explanation: The angle of elevation is used to calculate the height of a building from a point on the ground. This angle helps establish the relationship between the height and the distance from the building.

6. Q6Medium

   What is the angle of elevation when observing the top of a tower from a point 15 m away?

   • A.30°
   • B.45°
   • C.60°
   • D.75°
   Answer: 60°

   Explanation: The angle of elevation is the angle formed by the line of sight from the observer to the top of the tower with the horizontal. In this case, it is given as 60° when the observer is 15 m away from the tower.

7. Q7Medium

   What is the height of the tower if the angle of elevation from a point 30 m away is 30°?

   • A.10 m
   • B.15 m
   • C.20 m
   • D.25 m
   Answer: 15 m

   Explanation: Using the tangent ratio, tan(30°) = height/distance. Therefore, height = distance * tan(30°) = 30 * (1/√3) = 15 m.

8. Q8Medium

   What is the length of the ladder needed to reach a point 1.3 m below the top of a 5 m pole at an angle of 60°?

   • A.3.5 m
   • B.4.0 m
   • C.4.28 m
   • D.5.0 m
   Answer: 4.28 m

   Explanation: The height to be reached is 3.7 m (5 m - 1.3 m). Using the sine ratio, the length of the ladder (hypotenuse) can be calculated as 3.7/sin(60°) = 4.28 m.

9. Q9Medium

   How far should the foot of the ladder be placed from the pole if it is 4.28 m long and inclined at 60°?

   • A.1.5 m
   • B.2.14 m
   • C.3.0 m
   • D.4.0 m
   Answer: 2.14 m

   Explanation: Using the cosine ratio, the distance from the foot of the ladder to the pole can be calculated as 4.28 * cos(60°) = 2.14 m.

10. Q10Medium

    What is the width of the river if the bridge is 3 m high and the angles of depression to the banks are 30° and 45°?

    • A.5.0 m
    • B.6.196 m
    • C.7.5 m
    • D.8.0 m
    Answer: 6.196 m

    Explanation: Using the angles of depression, the width of the river can be calculated by adding the distances from the bridge to each bank, which involves using the tangent ratios for both angles.

11. Q11Medium

    What is the height of a kite flying at an angle of elevation of 60° from a point on the ground?

    • A.30 m
    • B.45 m
    • C.60 m
    • D.75 m
    Answer: 60 m

    Explanation: The height of the kite is directly given as 60 m above the ground, which is the vertical distance from the ground to the kite.

12. Q12Medium

    If the angle of elevation to the top of a cable tower from a 7 m high building is 60°, what is the height of the tower?

    • A.10.0 m
    • B.11.5 m
    • C.12.0 m
    • D.13.5 m
    Answer: 12.0 m

    Explanation: Using the tangent ratio, the height of the tower can be calculated as height = distance * tan(60°) + height of the building = 7 * √3 + 7 = 12.0 m.

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