STATIONS A AND B ARE 3(1+âˆš3) KM APART EACH STATION SIGHTS ON AIRPLANE AT ANGLE OF ELEVATION 30Â - Maths - Circles

Question

STATIONS A AND B ARE 3(1+âˆš3) KM APART EACH
STATION SIGHTS ON AIRPLANE AT ANGLE OF ELEVATION 30Â° AND
45Â° FIND THE ALTITUDE OF AIRPLANE ?

Koka Sri Lakshmi Divya Sai · Accepted Answer

$From the fig Let AD=h km BC=3 (1 + \sqrt{3}) k m Let BD=xkm and DC=3 (1 + \sqrt{3}) k m From Δ ABD {tan30}^{0} = \frac{AB}{BD} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{x} \Rightarrow x = h \sqrt{3} From Δ ADC \tan 45^{0} = \frac{AD}{DC} \Rightarrow 1 = \frac{h}{3 (1 + \sqrt{3}) - x} \Rightarrow h = 3 (1 + \sqrt{3}) - h \sqrt{3} (∵ h \sqrt{3} = x) \Rightarrow h \sqrt{3} + h = 3 (1 + \sqrt{3}) \Rightarrow h (1 + \sqrt{3}) = 3 (1 + \sqrt{3}) \Rightarrow h = 3 k m ∴ altitude of airplane=3km$

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STATIONS A AND B ARE 3(1+√3) KM APART. EACH STATION SIGHTS ON AIRPLANE AT ANGLE OF ELEVATION 30° AND 45°. FIND THE ALTITUDE OF AIRPLANE ?