Question : The thread of a kite makes an angle of 60° with the horizontal plane. If the length of the thread is 80 m, then the vertical height of the kite will be:

Option 1: $\frac{40}{\sqrt{3}}$ metres

Option 2: $\frac{80}{\sqrt{3}}$ metres

Option 3: $80$ metres

Option 4: $40\sqrt{3}$ metres

Question : If the angle of elevation of the sun decreases from $45^\circ$ to $30^\circ$, then the length of the shadow of a pillar increases by 60 m. The height of the pillar is:

Option 1: $60(\sqrt{3}+1)$ metres

Option 2: $30(\sqrt{3}–1)$ metres

Option 3: $30(\sqrt{3}+1)$ metres

Option 4: $60(\sqrt{3}–1)$ metres

Question : The angle of elevation of an aeroplane as observed from a point 30 metres above the transparent water surface of a lake is 30° and the angle of the depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water surface of the lake is:

Option 1: 60 metres

Option 2: 45 metres

Option 3: 50 metres

Option 4: 75 metres

Question : The value of $\frac{5 \cos ^2 60^{\circ}+4 \sec ^2 30^{\circ}-\tan ^2 45^{\circ}}{\tan ^2 60^{\circ}-\sin ^2 30^{\circ}-\cos ^2 45^{\circ}}$ is:

Option 1: $\frac{67}{27}$

Option 2: $\frac{22}{9}$

Option 3: $\frac{67}{24}$

Option 4: $\frac{19}{9}$

Question : The upper part of a tree broken at a certain height makes an angle of 60° with the ground at a distance of 10 metres from its foot. The original height of the tree was:

Option 1: $20\sqrt{3}$ metres

Option 2: $10{\sqrt3}$ metres

Option 3: $10\left (2+{\sqrt3} \right)$ metres

Option 4: $10\left (2-{\sqrt3}\right)$ metres