Question

A flagpole is erected at the top of a building. The angle of elevation of the top and foot of the flagpole from a point 100 m away, on the same level as that of the foot of the building, are 33° and 31° respectively. Find the height of the flagpole. Give your answer correct to the nearest metre.

(Use Mathematical Tables for this question.)

Answer 1

Let height of building (BC) be h meters and height of flagpole (CD) be x meters.

Distance from point = 100 m

In triangle ABC,

⇒ tan 31° = `(BC)/(AB)`

⇒ 0.6009 = `h/100`

⇒ h = 0.6009 × 100

⇒ h = 60.09 m

In triangle ADB,

⇒ tan 33° = `(DB)/(AB)`

⇒ tan 33° = `(h + x)/100`

⇒ h + x = 0.6494 × 100

⇒ 60.09 + x = 64.94

⇒ x = 64.94 − 60.09

⇒ x = 4.85 m ≈ 5 m

Hence, the height of flagpole = 5 m.