The angle of elevation of a cloud from a point h metres above a lake is theta.the angle of depression of its reflection in the lake is 45 degree.Find the height of the cloud?

Asked by pkirankumar4321 | 29th Nov, 2015, 01:26: PM

Expert Answer:

Let space straight A space be space the space position space of space the space cloud space and space straight B space be space the space position space of space its space reflection space in space lake. Let space straight E space be space the space point space straight h space metres space above space the space lake space making space angle space of space elevation space empty set space with space straight A space and space angle space of space depression space 45 degree space with space straight B. Let space straight x space be space the space height space of space cloud. From space the space figure space we space can space see space that comma EF space equals space DC space equals straight h comma AC space equals BC space equals straight x AD space equals space straight x minus straight h BD space equals straight x space plus space straight h  In increment AED comma tan empty set equals AD over ED equals fraction numerator straight x minus straight h over denominator ED end fraction...... left parenthesis 1 right parenthesis  In increment ED B comma tan space 45 degree equals DB over ED equals fraction numerator straight x plus straight h over denominator ED end fraction ED space equals straight x plus straight h....... left parenthesis 2 right parenthesis  From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis tan empty set equals fraction numerator straight x minus straight h over denominator straight x plus straight h end fraction xtan empty set plus htan empty set equals straight x minus straight h straight x open parentheses tan empty set minus 1 close parentheses equals negative straight h open parentheses tan empty set plus 1 close parentheses straight x equals fraction numerator straight h open parentheses 1 plus tan empty set close parentheses over denominator open parentheses 1 minus tan empty set close parentheses end fraction straight x equals fraction numerator straight h open parentheses tan 45 degree plus tan empty set close parentheses over denominator open parentheses tan 45 degree minus tan empty set close parentheses end fraction equals straight h open parentheses tan 45 degree plus tan empty set close parentheses  Hence space height space of space the space cloud space is space straight h open parentheses tan 45 degree plus tan empty set close parentheses space straight m.

Answered by Vijaykumar Wani | 30th Nov, 2015, 10:59: AM