Question : A tower is broken at a point P above the ground. The top of the tower makes an angle of $60^\circ$ with the ground at Q. From another point R on the opposite side Q angle of elevation of point P is $30^\circ$. If QR = 180 m, what is the total height (in meters) of the tower?

Option 1: $90$

Option 2: $45\sqrt{3}$

Option 3: $45(\sqrt{3}+1)$

Option 4: $45(\sqrt{3}+2)$

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

Question : The angle of elevation of the top of a tower from the top of a building whose height is 680 m is $45^{\circ}$ and the angle of elevation of the top of the same tower from the foot of the same building is $60^{\circ}$. What is the height (in m) of the tower?

Option 1: $340(3 + \sqrt3)$

Option 2: $310(3 - \sqrt3)$

Option 3: $310(3 + \sqrt3)$

Option 4: $340(3 - \sqrt3)$

Question : TF is a tower with point F on the ground. The angle of elevation of T from A is $\tan\;x^{\circ}=\frac{2}{5}$ and AF = 200 m. The angle of elevation of T from a nearer point B is $y^{\circ}$ with BF = 80 m. The value of $y$ is:

Option 1: 60$^{\circ}$

Option 2: 30$^{\circ}$

Option 3: 75$^{\circ}$

Option 4: 45$^{\circ}$