Mathematics

From a boat, 300 m away from a vertical pillar, the angles of elevation of the top and the foot of a vertical pillar at the edge of the cliff are 55°40' and 54°20' respectively. Find the height of the pillar correct to the nearest metre.

Heights & Distances

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Answer

Let CD be the pillar and AD be the cliff.

From a boat, 300 m away from a vertical pillar, the angles of elevation of the top and the foot of a vertical pillar at the edge of the cliff are 55°40' and 54°20' respectively. Find the height of the pillar correct to the nearest metre. Model Question Paper - 3, Concise Mathematics Solutions ICSE Class 10.

From figure,

$\Rightarrow \text{tan 54° 20'} = \dfrac{AD}{AB} \\[1em] \Rightarrow 1.3933 = \dfrac{AD}{300} \\[1em] \Rightarrow AD = 1.3933 \times 300 = 417.99 \approx 418 \text{ m} \\[1em] \Rightarrow \text{tan 55° 40'} = \dfrac{AC}{AB} \\[1em] \Rightarrow 1.4641 = \dfrac{AC}{300} \\[1em] \Rightarrow AC = 1.4641 \times 300 = 439.23 \approx 439\text{ m} \\[1em]$

From figure,

CD = AC - AD = 439 - 418 = 21 m.

Hence, height of the pillar = 21 m.

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Mathematics

From a boat, 300 m away from a vertical pillar, the angles of elevation of the top and the foot of a vertical pillar at the edge of the cliff are 55°40' and 54°20' respectively. Find the height of the pillar correct to the nearest metre.

Heights & Distances

Answer

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Mathematics

From a boat, 300 m away from a vertical pillar, the angles of elevation of the top and the foot of a vertical pillar at the edge of the cliff are 55°40' and 54°20' respectively. Find the height of the pillar correct to the nearest metre.

Heights & Distances

Answer

Related Questions

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(i) mid-point of diagonal AC
(ii) mid-point of diagonal BD
(iii) slope of diagonal AC
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In the given figure, O and O' are centers of two circles, touching each other at point P. The common tangent at P meets a direct common tangent AB at M. Show that :
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