Question

If one sees the bottom of a tree at a 45-degree angle of descent from the top of a 30 m high tower, what is the distance between the tree and the tower?​

Answer 1

Answer:

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Answer 2

$Given \: Height \:of \:the \:Tower (AB) = 30\:m$

$Angle \:of \: depression \: \angle {DAC}=45\degree$

$\angle {BCA}= \angle {DAC} = 45\degree$

$Distance \: between \: foot \: of \:the \:tree$

$to \: foot \: of \: the \:Tower = BC \: m$

$Now, In \: \triangle {ABC} ,$

$tan \angle {BCA}= \frac{AB}{BC}$

$\implies tan 45\degree = \frac{30}{BC}$

$\implies 1 = \frac{30}{BC}$

$\implies BC = 30 \:m$

Therefore.,

$\red{ Distance \: between \: foot \: of \:the \:tree}$

$\red{ to \: foot \: of \: the \:Tower }\green{= 30 \: m}$

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