Answer for question no 39 - Maths - Some Applications of Trigonometry

Question

Answer for question no 39

Komal Garg · Accepted Answer

Dear Student, It should be 3600 root 3 metre not 3000 root 3 metre

Let C be the initial position of the plane above the ground and E the position of plane after 30 seconds Let the speed of the plane be ν m/sec Given ∠CAB = 60°, ∠EAD 30°, BC = DE = 3600 $\sqrt{3}$ m Distance covered by the plane in 30 sec = ν m/sec × 30 sec = 30 ν m (Distance = Speed × Time) ∴ CE = BD = 30ν m In ΔABC, $\tan 60 ° = \frac{BC}{AB} (∵ \tan θ = \frac{Perpendicular}{Base}) ∴ \sqrt{3} = \frac{3600 \sqrt{3} m}{AB}$ ⇒ AB = 3600 m In ΔADE, $\tan 30 ° = \frac{DE}{AD} = \frac{DE}{AB+ BD}$ $∴ \frac{1}{\sqrt{3}} = \frac{3600 \sqrt{3} m}{3600 m + 30 v m}$ ⇒ 3600 + 30 ν = 3600 × 3 ⇒ 30 ν = 10800 – 3600 = 7200 $\Rightarrow v = \frac{7200}{30} = 240$ Speed of the plane = 240 m/sec = $240 \times \frac{18}{5}$ km/hr = 864 km/hr Thus, the speed of the plane is 864 km/hr Cheers!

Answer for question no.39