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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$$=2+6=8m$$

1204095_1200075_ans_28f6b1cdbc304fb5b3f02f1b4a1cf918.png

Mathematics

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