From a window 15 metres high above the ground in a street, the angles of elevation and depression of the top and the…

CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2024 · Standard

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595 Marks · March 2024 · Standard

From a window $15$ metres high above the ground in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are $30^{\circ}$ and $45^{\circ}$ respectively. Find the height of the opposite house. (Use $\sqrt{3} = 1.732$)

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For correct figure
In right $\triangle BPC$,
$\tan 45^{\circ} = 1 = \frac{15}{x}$
$\Rightarrow x = 15$
In right $\triangle BPD$,
$\tan 30^{\circ} = \frac{h}{x}$
$h = \frac{15}{\sqrt{3}}$ or $5\sqrt{3}$
$\therefore$ Height of opposite house $(CD) = 5\sqrt{3} + 15$
$= 5 (1.732) + 15 = 23.66$ m