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An observer standing 72 m away from a building notices that the angles of elevation of the top and the bottom of a flagstaff on the building are respectively 60° and 45°. The height of the flagstaff is:

  1. 52.7 m

  2. 73.2 m

  3. 98.3 m

  4. 124.7 m

Heights & Distances

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Answer

An observer standing 72 m away from a building notices that the angles of elevation of the top and the bottom of a flagstaff on the building are respectively 60° and 45°. The height of the flagstaff is: Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Let BA be the flagstaff and BC be the building.

Let O be the position of observer.

In triangle OCB,

⇒tan⁡45∘=BCOC⇒1=BC72⇒BC=72 m.\Rightarrow \tan 45^{\circ} = \dfrac{BC}{OC} \\[1em] \Rightarrow 1 = \dfrac{BC}{72} \\[1em] \Rightarrow BC = 72 \text{ m}.

In triangle OCA,

⇒tan⁡60∘=ACOC⇒3=AC72⇒AC=723 m.\Rightarrow \tan 60^{\circ} = \dfrac{AC}{OC} \\[1em] \Rightarrow \sqrt3 = \dfrac{AC}{72} \\[1em] \Rightarrow AC = 72\sqrt3 \text{ m.}

The height of the flagstaff is

AB = AC - BC

= 72 3\sqrt{3} - 72

= 72(3\sqrt{3} - 1)

= 72(1.732 - 1)

= 72(0.732)

= 52.7 m.

Hence, option 1 is the correct option.

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