Some Applications of Trigonometry: CBSE Class 10 Previous Year Questions

From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be $45^{\circ }$. The height (in metres) of the tower is :

1. (A)$10\sqrt{3}$
2. (B)$30\sqrt{3}$
3. (C)60
4. (D)30

If the length of the shadow of a tower is $\sqrt{3}$ times that of its height, then altitude of the Sun is :

1. (A)$45^{\circ }$
2. (B)$30^{\circ }$
3. (C)$60^{\circ }$
4. (D)$15^{\circ }$

A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as $60^{\circ }$. If AB = $5\sqrt{3}$ m, then length of the wire is

1. (A)10 m
2. (B)$10\sqrt{3}$ m
3. (C)15 m
4. (D)$\frac{5}{2}\sqrt{3}$ m

Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections 'A' and 'B'. Tower is supported by wires from a point 'O' (as shown in figure).
Distance between the base of the tower and point 'O' is 6 m. From point 'O', the angle of elevation of the top of the section 'B' is $30^{\circ }$ and the angle of elevation of the top of section 'A' is $60^{\circ }$.
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'. (1)
(ii) Find the length of the wire from the point 'O' to the top of section 'A'. (1)
(iii) (a) Find the distance AB. (2)
OR
(iii) (b) Find the area of $△OPB$. (2)

Tejas is standing at the top of a building and observes a car at an angle of depression of $30^{\circ }$ as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to $60^{\circ }$, and at that moment, the car is 25 m away from the building.
Based on the information given above, answer the following questions :
(i) What is the height of the building ? (1)
(ii) What is the distance between the two positions of the car ? (1)
(iii) (a) What would be the total time taken by the car to reach the foot of the building from the starting point ? (2)
OR
(iii) (b) What is the distance of the observer from the car when it makes an angle of $60^{\circ }$ ? (2)

Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is 54 metres away from the water tank.
From a window (W) of the building, the angle of elevation of top of the tank is $45^{\circ }$ and angle of depression of its foot is $30^{\circ }$.
(i) Write a relation between d (the height of window) and y. (1)
(ii) Determine the value of h. (1)
(iii) (a) Determine height of the water tank. (2)
OR (iii) (b) Find the value of $x$ and height of the window above ground level. (2)

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ }$ and $30^{\circ }$ respectively. Find the height of the poles and the distance of the point from the poles.

A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as $30^{\circ }$. From the bottom of the same building, the angle of elevation of kite is $45^{\circ }$. Find the length of the string and height of roof from the ground. (Use $\sqrt{3}=1.73$)

In the given figure, which of the following angles represents the angle of depression ?

1. (A)$x$
2. (B)$y$
3. (C)$z$
4. (D)$a$

The length of the shadow of a tower when the sun’s altitude changes from $30^{\circ }$ to $60^{\circ }$ will :

1. (A)become shorter
2. (B)become longer
3. (C)remain same
4. (D)be doubled