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Mathematics

From a boat, 200 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the edge of the cliff are 36° and 34° respectively. Find:

(i) the height of the cliff, and

(ii) the height of the pillar.

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Answer

(i) Let AB be the cliff, BC be the pillar and O be the point of observation.

Then, ∠AOB = 34°, ∠AOC = 36° and OA = 200 m

From a boat, 200 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the edge of the cliff are 36° and 34° respectively. Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

In △AOB,

⇒tan⁡34°=PerpendicularBase=ABOA⇒0.6745=AB200⇒AB=(0.6745×200)⇒AB=134.9 m.\Rightarrow \tan 34° = \dfrac{\text{Perpendicular}}{\text{Base}} = \dfrac{AB}{OA} \\[1em] \Rightarrow 0.6745 = \dfrac{AB}{200} \\[1em] \Rightarrow AB = (0.6745 \times 200) \\[1em] \Rightarrow AB = 134.9 \text{ m.}

Hence, height of the cliff 134.9 m.

(ii) In △AOC,

⇒tan⁡36°=PerpendicularBase=ACOA⇒0.726=AC200⇒AC=(0.726×200)⇒AC=145.2 m.\Rightarrow \tan 36° = \dfrac{\text{Perpendicular}}{\text{Base}} = \dfrac{AC}{OA} \\[1em] \Rightarrow 0.726 = \dfrac{AC}{200} \\[1em] \Rightarrow AC = (0.726 \times 200) \\[1em] \Rightarrow AC = 145.2 \text{ m.}

Height of pillar = AC - AB = 145.2 - 134.9 = 10.3 m

Hence, height of the pillar 10.3 m.

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