If a man of height 150 cm standing at point P has 60° angle of elevation from his foot and 30° angle of elevation from his head, then find the height of lighthouse which is point A.?

Option 2 : 225 cm

Given,

[ alt="Assign 4 Kajal 18April 32Q हिंदी हरीश uploding nita 2" src="//storage.googleapis.com/tb-img/production/19/05/Assign_4_Kajal_18April_32Q_%E0%A4%B9%E0%A4%BF%E0%A4%82%E0%A4%A6%E0%A5%80%20%E0%A4%B9%E0%A4%B0%E0%A5%80%E0%A4%B6_uploding_nita_2.PNG">

In ΔAQP,

⇒ tan 60° = AQ/PQ

⇒ √3 = AQ/PQ

⇒ AR + RQ = PQ(√3)

In ΔARS,

⇒ tan 30° = AR/SR

⇒ 1/√3 = AR/SR

As, SR = PQ

⇒ 1/√3 = AR/PQ

Then,

⇒ AR + RQ = PQ√3

⇒ AR/PQ + RQ/PQ = (√3)

⇒ 1/√3 + 150/PQ = (√3)

⇒ 1 + 150√3/(PQ) = 3

⇒ PQ = 75√3

Then,

⇒ √3 = AQ/(75√3)

⇒ AQ = 225cm

∴ Height of the lighthouse = 225 cm