Question

# The lower window of a house is at height of $$2\;m$$ above the ground and its upper windowis $$4\;m$$ vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows windows are observed tom be $$60^{\circ}$$ and $$30^{\circ}$$, respectively. Find the height of the balloon above the ground.

Solution

## $$\tan { 60° } =\cfrac { 4+{ h }_{ 1 } }{ x } \Rightarrow \sqrt { 3 } =\cfrac { 4+{ h }_{ 1 } }{ x } \rightarrow 1$$$$\tan { 30° } =\cfrac { { h }_{ 1 } }{ x } \Rightarrow \cfrac { 1 }{ \sqrt { 3 } } =\cfrac { { h }_{ 1 } }{ x } \rightarrow 2$$Dividing equations $$2/1$$$$\cfrac { 1 }{ \sqrt { 3 } \times \sqrt { 3 } } =\cfrac { { h }_{ 1 }\times x }{ x\left( 4+{ h }_{ 1 } \right) }$$$$\Rightarrow 3{ h }_{ 1 }=4+{ h }_{ 1 }$$$$\Rightarrow 2{ h }_{ 1 }=4$$$${ h }_{ 1 }=2$$Height of balloon$$=2+6=8m$$Mathematics

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