Question

an observer 1.5 metre tall is 30 M away from a Chimney the angle of elevation of the top of the chimney from his eye is 60 degree find the height of the chimney

Answer 1

Answer:

$\red {Height \:of \:the \: Chimney}\green {= 53.46\:m}$

Step-by-step explanation:

Height of the observer (AB) = 1.5 m,

Height of the Chimney (CE) = h m,

Distance from observer to foot of the chimney (CB) = 30 m,

Angle of elevation <DAE = 60°,

Let ED = x ,

AB = CD = 1.5 m,

CB = AD = 30 m,

$In \: \triangle ADE , \:\angle DAE = 60\degree$

$tan \:60\degree = \frac{ED}{DA}$

$\implies \sqrt{3} = \frac{x}{30}$

$\implies 30\sqrt{3} = x$

$Height \:of \:the \: Chimney (h) = CD + x \\= 1.5 \:m + 30\sqrt{3}\\= 1.5 + 30 \times 1.732 \\= 1.5 + 51.96\\= 53.46\:m$

Therefore.,

$\red {Height \:of \:the \: Chimney}\green {= 53.46\:m}$

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