Class 10 Some Applications of Trigonometry Previous Year Questions

    Q1:

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    Radio towers are used for transmitting a range of communication services including radio and television. The tower will eighter act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was build in two Sections A and B. Tower is supported by wires from a point O.Distance between the base of the tower and point O is 36cm. From point O, the angle of elevation of the top of the Section B is 30° and the angle of elevation of the top of Section A is 45°. Based on the above information, answer the following questions: (i) Find the length of the wire from the point O to the top of Section B. (ii) Find the distance AB. OR Find the are of ∆OPB. (iii) Find the height of the Section A from the base of the tower.

    CBSE [2023]

    Medium

    Q2:

    From a point on the ground, the angle of elevation of the bottom and top of a transmission tower fixed at the top of 30 m high building are 30° and 60°, respectively. Find the height of the transmission tower. (Use √3 = 1.73)

    CBSE [2023]

    Medium

    Q3:

    As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 60°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use √3 = 1.73)

    CBSE [2023]

    Easy

    Q4:

    The length of the shadow of a tower on the plane ground is 3 times the height of the tower. Find the angle of elevation of the sun.

    CBSE [2023]

    Easy

    Q5:

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    A spherical balloon of radius r subtends an angle of 60° at the eye of an observer. If the angle of elevation of its centre is 45° from the same point, then prove that height of the centre of the balloon is √2 times its radius.

    CBSE [2023]

    Hard

    Q6:

    An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the stance between the two planes at that instant.

    CBSE [2022]

    Medium

    Q7:

    A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Ten seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

    CBSE [2022]

    Hard

    Q8:

    The tops of two poles of heights 20 m and 28 m are connected with a wire. The wire is inclined to the horizontal at an angle of 30°. Find the length of the wire and the distance between the two poles.

    CBSE [2022]

    Medium

    Q9:

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    In Fig, AB is tower of height 50m. A man standing on its top, observes two cars on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the two cars.

    CBSE [2022]

    Easy

    Q10:

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    Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14th century. The lake has many Chhatris. One of them is shown above : Observe the picture. From a point A h m above from water level, the angle of elevation of top of Chhatri (point B) is 45 and angle of depression of its reflection in water (point C) is 60 . If the height of Chhatri above water level is (approximately) 10 m, then (a) draw a well-labelled figure based on the above information (b) find the height (h) of the point A above water level. (Use √3 = 1·73)

    CBSE [2022]

    Medium

    Q11:

    From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30 and 45respectively. If the bridge is at a height of 3 m from the banks, then find the width of the river.

    CBSE [2022]

    Medium

    Q12:

    The angle of elevation of the top of a building from the foot of the tower is 30 and the angle of elevation of the top of the tower from the foot of the building is 60 . If the tower is 50 m high, then find the height of the building.

    CBSE [2022]

    Easy