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[tex]\huge{\mathfrak{\underline{\underline{Question}}}}[/tex]
[tex]\sf{\large{Don't\: Spam}}[/tex]
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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!