Question

A telephone tower stands on a top of the building, a 2 m tall person
stand 5 m away from the foot of the building and he observes the
top of the tower and foot of the tower at the angles of elevation 60°
and 45°, find the heights of the building and tower.​

Answer 1

According to the problem,

Height of the person (AB) = 2 m,

Height of the building (CE) = ( 2+x) m,

Height of the tower (EF) = h m ,

Distance from person to foot of the building (BC) = 5 m ,

$In \: \triangle ADE , \:we \:have , \\</p><p>tan 45\degree = \frac{DE}{AD} \\\implies 1 = \frac{x}{5} \\\implies x = 5 \:m \: ---(1)$

$In \: \triangle ADF , \:we \:have , \\</p><p>tan 60\degree = \frac{DF}{AD} \\\implies \sqrt{3} = \frac{x+h}{5} \\\implies 5\sqrt{3}= (5+h) \:m$

$\implies h = 5\sqrt{3} - 5$

$\implies h = 5(\sqrt{3} - 1)$

$\implies h = 5(1.732- 1)$

$\implies h = 5 \times 0.732$

$\implies h = 3.66\: m\: ---(2)$

$Now, Height \: of \:the \: building = 2 + x \\= 2+ 5\\= 7 \: m$

Therefore.,

$\red { Height \:of \:the \:tower } \green {= 3.66 \:m }$

$\red { Height \:of \:the \: building } \green {= 7 \:m }$

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Answer 2

Step-by-step explanation:

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thank you .