Question

The angle of elevation of the top of a tower from a point on the ground and at a distance of 150 m from its foot is 300. Find the height of the tower correct to one place of decimal.​

Answer 1

Solution :-

Consider BC as the tower and A as the point on the ground such that.

↪ ∠A = 30° and AC = 150 m

• [ Refer to the attachment ]

Take x m as the height of the tower

• We know that,

↪tan θ = BC/AC

• Substituting the values

↪tan 30° = x/150

• By cross multiplication

↪1/√3 = x/150

• So we get,

↪x = 150/√3

• Multiplying and dividing by √3

↪x = (150 × √3)/ (√3 × √3)

• By further calculation

↪x = 150√3/ 3 = 50√3 m

• Substituting the value of √3

↪x = 50 (1.732)

↪x = 86.600 m

↪x = 86.6 m

Hence,

• The height of the tower is 86.6m.