Question : The length of the shadow of a vertical pole on the ground is 36 m. If the angle of elevation of the sun at that time is $\theta$. Such that $\sec \theta=\frac{13}{12}$, then what is the height (in m) of the pole?

Option 1: 12

Option 2: 15

Option 3: 18

Option 4: 9

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

Option 1: 18

Option 2: 7.5

Option 3: 13

Option 4: 19.5

Question : A ladder leaning against a wall makes an angle $\theta$ with the horizontal ground such that $\tan \theta=\frac{12}{5}$. If the height of the top of the ladder from the wall is 24 m, then what is the distance (in m) of the foot of the ladder from the wall?

Option 1: 18

Option 2: 19.5

Option 3: 7.5

Option 4: 10

Question : If the height of a pole is $2\sqrt{3}$ metres and the length of its shadow is 2 metres, then the angle of elevation of the sun is:

Option 1: 90°

Option 2: 45°

Option 3: 30°

Option 4: 60“

Question : A pole of length 7 m is fixed vertically on the top of a tower. The angle of elevation of the top of the pole observed from a point on the ground is 60° and the angle of depression of the same point on the ground from the top of the tower is 45°. The height (in m) of the tower is:

Option 1: $7(2 \sqrt{3}-1)$

Option 2: $\frac{7}{2}(\sqrt{3}+2)$

Option 3: $7 \sqrt{3}$

Option 4: $\frac{7}{2}(\sqrt{3}+1)$