Question

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The
angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30º. Find the distance travelled by the balloon during the interval.​

Answer 1

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⎟⎟ ✪✪ ＱＵＥＳＴＩＯＮ ✪✪⎟⎟

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30º. Find the distance travelled by the balloon during the interval.

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⎟⎟ ✰✰ ＡＮＳＷＥＲ ✰✰ ⎟⎟

✿✿ ʀᴇғᴇʀ ᴛᴏ ɪᴍᴀɢᴇ ғɪʀsᴛ ✿✿

◆ $\tt\footnotesize{Height \:of \:the \:balloon \:from\: tower\:= \:88.2m}$

◆ $\tt\footnotesize{Height\:of\:the\:girl\: =\: 1.2 m}$

◆ $\tt\footnotesize{Angles\:of\: elevations\:=\:60° \:and\: 30°}$

◆ $\tt\footnotesize{Let\:the\:distance\:travelled\:=\: d m}$

$\tt\huge{From\:the\:figure}$

$\tt{tan\:60°\:= \:\frac{87}{x}}$

➜$\:\:$ $\tt{\sqrt{3}\:=\:\frac{87}{x}}$

➜$\:\:$$\tt{87 \:= \:\sqrt{3 x}}$ ━━━━ ➀

➜$\:\:$$\tt{x\:=\:\frac{87}{\sqrt{3}}m}$

$\tt{Also\:30°\:=\:\frac{87}{x\:+\:d}}$

➜$\:\:$$\tt{\frac{1}{\sqrt3}\:=\:\frac{87}{(x\:+\:d)}}$

➜$\:\:$$\tt{87\:=\:\frac{x\:+\:d}{\sqrt{3}}}$ ━━━━ ➁

ғʀᴏᴍ ➀ ᴀɴᴅ ➁

➜$\:\:$$\tt{\sqrt{3}x\:=\:\frac{x\:+\:d}{\sqrt{3}}}$

➜$\:\:$$\tt{\sqrt{3}.\sqrt{3}x\:=\:x\:+\:d}$

➜$\:\:$$\tt{3x\:=\:x\:+\:d}$

➜$\:\:$$\tt{2x\:=\:d}$

$\tt{Distance\:travelled\:=\:2\:×\:\frac{87}{\sqrt{3}}}$

➜$\:\:$$\tt{\frac{2\:×\:29\:×\:\sqrt{3}\:×\:\sqrt{3}}{\sqrt{3}}}$

➜$\:\:$$\tt{58\sqrt{3}m}$

⛬ The distance travelled by the balloon during the interval = $\huge\frak\pink{58\sqrt{3}\:m}$

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Answer 2

REFER TO ATTACHMENT......XD