# At the foot of a mountain the elevation of its summit is 45°.After ascending 1000m towards the top of the mountain at an angle of 30°,the elevation is found to be 60°.Find the height of the mountain.

1
by Abarrane

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by Abarrane

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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