Question

At the foot of the mountain, the elevation of its summit is 45°. After going up at a distance of 1km towards the top of the mountain at an angle of 30°, the elevation changes to 60°. Find the height of the montain.​

Answer 1

Answer:

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Step-by-step explanation:

Let point A be the position of summit of the mountain and B being its foot.Let C be the original position of observer and D, the final position after ascending 1000 metres.Let DN and DM be perpendiculars to BC and AB respectively.Thus,

CD = 1000 m  

∠DCN = 30⁰  

and, ∠ADM = 60⁰

∠ACB = 45⁰ = ∠ACB  

∠DAM = 30°  

⇒ ∠DCA = 15° , ∠DAC = 15°

⇒ ∠DCA = ∠DAC  

⇒AD=CD = 1000 m

now,  

In right Δ DCN  

sin 30° = DN/CD  

⇒1/2 = DN/1000

⇒ DN = 500 m  

And, In right Δ ADM  

sin 60° = AM/AD  

⇒ √3/2 = AM/1000  

⇒AM = 500 √3 = 500 × 1.732 = 866

⇒AM = 866 m  

TOTAL HEIGHT (AB) = BM + AM = DN + AM = 500 + 866 = 1366 m = 1.36.6 KM