A boy who is 1.75m tall, is flying a kite, when the length of the string of kite is 150m, it makes an angle of 30° with the horizon. What is the height of the kite from the ground?
Answers
Answered by
75
Answer:
- The height of Kite from land is 76.75m.
Step-by-step Explanation:
Given,
- Height of Boy (AP) = 1.75m
- Length of string (AC) = 150m
- Angle of horizon = 30°
Here,
- We find A Right angled ∆ ABC.
- And, Angle given (θ) = 30°
- P (Opposite to θ) = BC
H (Hypotenuse) = AC
- H = 150m
As we know that,
- ➺ sin θ = P/H
- ➺ sin 30° = BC/AC
- ➺ 1/2 = BC/150m
- ➺ 2BC = 150m
- ➺ BC = 75m
In adjoining figure,
- As QC is straight line.
We can say that,
- ➺ ∠ABC + ∠ABQ = 180° •••[LP]
- ➺ 90° + ∠ABQ = 180°
- ➺ ∠ABQ = 90° •••[1]
As AP and BQ is perpendicular to land.
So,
We can say that,
- ∠APQ = 90° and ∠BQP = 90° •••[2]
As ABQP is a Quadrilateral.
So,
- ➺ ∠ABQ + ∠BQP + ∠APQ + ∠PAB = 360° •••[ASPO Quadrilateral]
- ➺ 90° + 90° + 90° + ∠PAB = 360°
- ➺ 270° + ∠PAB = 360°
- ➺ ∠PAB = 90° •••[3]
By [1], [2] and [3],
We can say that,
- ABQP is a Rectangle.
And,
- AP = BQ •••[Opposite side of Rectangle are equal]
- ➺ BQ = 1.75m
- QC = BQ + BC •••[As given in figure]
- ➺ QC = 1.75m + 75m
- ➺ QC = 76.75m
As QC is the height of Kite from land.
Therefore,
- The height of Kite from land is 76.75m.
Attachments:
Answered by
1
Step-by-step explanation:
Answer: Height of the kite is 75√3 m.
Step-by-step explanation:
Since we have given that
Length of string of kite = 150 m
Angle of elevation formed by a kite with the horizontal = 60°
We need to find the height of kite.
Consider Δ ABC, as shown in the figure:
Attachments:
Similar questions