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A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression 30°. After some time angle of depression becomes 60°. What is the distance travelled by car during this time?
- a)100√3 m
- b)200√3/3 m
- c)100√3/3 m
- d)200√3 m
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A man from the top of a 100 m high tower sees a car moving towards the...
In the figure,
The car’s position changes from B to D and it travelled ‘x’ m;
In ΔACD;
tan 60° = 100/AD
⇒ √3 = 100/AD
⇒ AD = 100/√3 m
In ΔABC;
tan 30° = 100/AB
⇒ 1/√3 = 100/AB
⇒ AB = 100√3 m
∴ x = AB – AD = 100√3 – 100/√3 = 200/√3 = 200√3/3 m
∴ Distance travelled by car during this time = 200√3/3 m
Most Upvoted Answer
A man from the top of a 100 m high tower sees a car moving towards the...
The angle of depression is the angle between the line of sight from the top of the tower to the car and the horizontal ground. In this case, the angle of depression is 30 degrees.
We can use trigonometry to find the horizontal distance between the car and the tower. Let's call this distance x.
In a right triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the opposite side is the height of the tower (100 m) and the adjacent side is the horizontal distance (x).
Using the tangent function, we can write the equation:
tan(30 degrees) = 100 m / x
To find x, we can rearrange the equation:
x = 100 m / tan(30 degrees)
Using a calculator, we can evaluate the tangent of 30 degrees:
tan(30 degrees) ≈ 0.577
Substituting this value into the equation, we get:
x = 100 m / 0.577 ≈ 173 m
Therefore, the horizontal distance between the car and the tower is approximately 173 meters.
We can use trigonometry to find the horizontal distance between the car and the tower. Let's call this distance x.
In a right triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the opposite side is the height of the tower (100 m) and the adjacent side is the horizontal distance (x).
Using the tangent function, we can write the equation:
tan(30 degrees) = 100 m / x
To find x, we can rearrange the equation:
x = 100 m / tan(30 degrees)
Using a calculator, we can evaluate the tangent of 30 degrees:
tan(30 degrees) ≈ 0.577
Substituting this value into the equation, we get:
x = 100 m / 0.577 ≈ 173 m
Therefore, the horizontal distance between the car and the tower is approximately 173 meters.
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A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression 30°. After some time angle of depression becomes 60°. What is the distance travelled by car during this time?a)100√3 mb)200√3/3 mc)100√3/3 md)200√3 mCorrect answer is option 'B'. Can you explain this answer?
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