Question

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Answer 1

Answer:

3.29 km

Step-by-step explanation:

Let A be the mountain top and C,D are the points of observation.

(i)

In ΔABC,

Tan 25° 10' = AB/BC

⇒ BC tan 25° 10' = AB

⇒ BC = AB/tan 25° 10'

⇒ BC = AB/0.47

(ii)

In ΔABD,

tan 15° 20' = AB/BD

⇒ tan 15° 20' = AB/BC + 5 {Given,distance = 5 km}

⇒ 0.2742 = AB/BC + 5

Substitute (i) in (ii), we get

⇒ 0.47AB = 0.2742(AB + 2.35)

⇒ 0.47AB = 0.2742AB + 0.644

⇒ 0.1958AB = 0.644

⇒ AB = 3.29 km.

Therefore, height of the mountain = 3.29 km.

Hope it helps!