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CBSE Class 10 Answered

if the angle of elevation of a cloud from a point h meters above a lake is alpha and the angle of depression of its reflection in the lake is beta, prove that the height of the cloud is  h(tan beta + tan alpha)/(tan beta - tan alpha)
Asked by deepakkumar12870 | 22 Feb, 2019, 08:11: PM
answered-by-expert Expert Answer
Figure shows the angle of elevation of cloud and angle of depression of its image in the Lake as observed from a height h.
 
Let H be the height of cloud from the observation level.
 
from figure we have,  tanα = H/L     and  tanβ = (2h+H)/L
 
By eliminating L from the above relations, we have H×cotα = (2h+H)cotβ  or  H×(cotα - cotβ) = 2h×cotβ
 
begin mathsize 12px style H open parentheses fraction numerator 1 over denominator tan alpha end fraction space minus space fraction numerator 1 over denominator tan beta end fraction close parentheses space equals space fraction numerator 2 h over denominator tan beta end fraction H open parentheses fraction numerator tan beta space minus space tan alpha over denominator tan alpha space tan beta end fraction close parentheses space equals space fraction numerator 2 h over denominator tan beta end fraction H space equals space fraction numerator 2 h space tan alpha over denominator open parentheses tan beta space minus space tan alpha close parentheses end fraction end style
 
Cloud Height = begin mathsize 12px style H plus h space equals space fraction numerator 2 h tan alpha over denominator open parentheses tan beta space minus space tan alpha close parentheses end fraction space plus space h space equals space fraction numerator h open parentheses tan alpha space plus space tan beta close parentheses over denominator open parentheses tan beta space minus space tan alpha close parentheses end fraction end style
Answered by Thiyagarajan K | 23 Feb, 2019, 05:47: PM

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