11)

A ladder 10 m long rests against a vertical wall making an angle of 30° with the wall. How high up (in m) does it reach the wall from the ground? (Take \(\sqrt 3 = 1.73.\))

SSC CHSL 2021

A)

8.56

B)

8.65

C)

5.88

D)

5

12)

At a particular time, the length of the shadows of a pole and that of a tower are, respectively, 12 m and 27 m. If the height of the pole is 24 m, what is the height (in m) of the tower?

SSC Selection Post Matric 2022

A)

54

B)

63

C)

45

D)

36

13)

A person was standing on a road near a mall. He was 1425 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The height of the tree is 10 m and it is 30 m away from him. How tall (in m) is the mall?

SSC CPO 2020

A)

475

B)

300

C)

525

D)

425

14)

A ladder leaning against a wall makes an angle θ with the horizontal ground such that \( \cos \theta = \dfrac{5}{13} \). If the height of the top of the ladder from the foot of the wall is 18 m, then what is the distance (in m) of the foot of the ladder from the wall?

SSC CPO 2020

A)

19.5

B)

7.5

C)

13

D)

18

15)

The length of the shadow of a vertical pole on the ground is 18 m. If the angle of elevation of the sun at that time is θ, such that \(\cos \theta = \frac {12}{13} \), then what is the height (in m) of the pole?

SSC CPO 2020

A)

7.5

B)

9

C)

18

D)

12

16)

Asha and Suman's mud forts have heights 9 cm and 16 cm. They are 24 cm apart. How far (in cm) are the fort tops from each other?

SSC CPO 2020

A)

25

B)

16

C)

24

D)

7

17)

The length of the shadow of a vertical pole on the ground in 36 m. If the angle of elevation of the sun at that time is θ, such that secθ = (13/12) then what is the height (in cm) of the pole?

SSC CPO 2020

A)

12

B)

15

C)

18

D)

9

18)

Asha and Suman's mud forts have heights 9 cm and 16 cm. If the fort tops are at 25 cm apart from each other, then the distance (in cm) between two forts is:

SSC CPO 2020

A)

7

B)

16

C)

25

D)

24

19)

A ladder is resting against a wall. The angle between the foot of the ladder and wall is 60°, and the foot of the ladder is 3.6 m away from the wall. The length of the ladder (in m) is:

SSC CPO 2020

A)

5.4

B)

14.4

C)

3.6

D)

7.2

20)

Let A and B be two towers with same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 60°, respectively. The ratio of the heights of B and A is:

SSC CPO 2020

A)

3 : 1

B)

1: √ 3

C)

1 : 2

D)

1 : 3