Question

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of top of the tower from the foot of the hill is 30°.If the tower is 50 m high, what is the height of the hill?​

Answer 1

Answer:

here is ur answer hope you understand

Answer 2

Given :-

• The angle of elevation of top of a hill at the foot of tower = 60°
• The angle of elevation of top of the tower at the foot of hill = 30°
• The height of the tower = 50 m

To Find :-

The height of the hill = ?

Solution :-

To calculate the height of hill at first we have to use trigonometry ratio to set up equation. As per the given clue in the question. According to figures , we have to assume CD be h and BC is horizontal base of hill and tower. And AB is Tower with height 50m high. Here we will solve the problem by take clue and the clues are The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of top of the tower from the foot of the hill is 30°.If the tower is 50 m high. Simply by Applying trigonometry ratio to calculate the height of hill. As per the figure relation make with tan because calculation based on perpendicular and base.

Calculation begins :-

⟼ In right angle ∆ ABC

AB = 50m. Angle ACB = 30°

⟼ Tan A = AB/BC

⟼ Tan 30° = 50/BC

⟼ 1/√3 = 50/BC

⟼ BC × 1 = 50 × √3

⟼ BC = 50√3 ---------(i)

⟼ In right angle ∆ BCD

CD = h. Angle DBC = 60°

⟼ Tan A = CD/BC

⟼ Tan 60° = h/BC

⟼ √3 = H/BC

⟼ H = BC√3 ---------(ii)

Now putting the value of BC in eq (ii):-

⟼ H = BC × √3

⟼ H = 50√3 × √3

⟼ H = 50 × √9

⟼ H = 50 × 3

⟼ H = 150m

Hence,

The height of hill = 150 m

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