Math, asked by mahnoor7419, 8 months ago

A castle stands on top of a mountain. At a point on level ground which is 55 m away from the foot of the mountain, the angle of elevation of the top of the castle and the top of the mountain are 60° and 45° respectively. Find the height of the castle.

Answers

Answered by RvChaudharY50
3

Given :- (From diagram)

  • BC = Height of mountain = H
  • AB = Height of castle = h .
  • CD = 55m .
  • ∠BDC = 45°
  • ∠ADC = 60° .

To Find :-

  • Height of castle = h ?

Solution :-

in Right ∆BCD, we have ,

→ Tan45° = BC/CD

→ 1 = H/55

→ H = 55m . --------- Eqn.(1)

in Right ∆ACD , we have,

→ Tan60° = AC/CD

→ √3 = (H + h) / 55

→ √3*55 = H + h

Putting value from Eqn.(1)

55√3 = 55 + h

→ h = 55√3 - 55

→ h = 55(√3 - 1)

→ h = 55(1.732 - 1)

→ h = 55 * 0.732

→ h = 40.26 m .(Ans.)

Hence, the height of the castle is 40.26m.

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