A flagstaff stands on the top of a building. At a distance of 30 m away from the foot of the building, the angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 30°. Find the height (in metres) of the flagstaff.

Correct option is A

Given:

Distance from building = 30 m

Angle of elevation to top of building = 30°

Angle of elevation to top of flagstaff = 60°

Find height of flagstaff.

Formula Used:

$$\tan\theta$$​ = $$\frac{Perpendicular}{Base}$$​​

Solution:

Height of building

​$$\tan 30^\circ = \frac{BC}{30} \\\ \\ \frac{1}{\sqrt{3}} = \frac{BC}{30} \\\ \\BC = \frac{30}{\sqrt{3}} = 10\sqrt{3}$$m​

Total height (building + flagstaff)

​$$\tan 60^\circ = \frac{BF}{30} \\ \ \\\sqrt3 =\frac{BF}{30}\\ \ \\BF = 30\sqrt{3}$$​​

Flagstaff height = BF - BC

​$$= 30\sqrt{3} - 10\sqrt{3} \\\ \\= 20\sqrt{3} \ m$$​​