A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the the bottom of the first house is 30° . If the distance between the two houses is 6 textm then the height of the first house is (in m )

Question

A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the the bottom of the first house is 30° . If the distance between the two houses is 6 textm then the height of the first house is (in m ) (A) 8 √3 (B) 16 √3 (C) 3 √3 (D) 12 √3

Tardigrade Admin · Accepted Answer

Let textitD be the position of window of second house and textitBC be the position of the first house. <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-zxbi2ate0xswmdq2.jpg" /> In textÎ textitADB , textitAD=2√3 textitBD=4√3 In textÎ textitBCD , textcos60° =( textitBD/ textith) ∴ textith=8√3

Q. A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the the bottom of the first house is $3 0^{^{\circ}}$ . If the distance between the two houses is $6$ $m$ then the height of the first house is (in $m$ )

$83$

$163$

$33$

$123$

Let $D$ be the position of window of second house and $BC$ be the position of the first house.

In $Δ ADB$ , $AD = 23$
$BD = 43$
In $Δ BCD$ ,
$cos 6 0^{^{\circ}} = \frac{BD}{h}$
$∴ h = 83$

Q. A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the the bottom of the first house is 30∘ . If the distance between the two houses is 6 m then the height of the first house is (in m )

83​

163​

33​

123​