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The height of a light house is 20 meters above sea level. The angle of depression (from the top of the lighthouse) of a ship in the sea is 30°. What is the distance of the ship from the foot of the light house?
- a)16 m
- b)20√3 m
- c)20 m
- d)30 m
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The height of a light house is 20 meters above sea level. The angle of...
From the given data,
Let AB be the height of the light house = 20 m and BC be the distance between foot of the light house to the ship
From the figure, we get
tan 30° = AB/BC
⇒ 1/√3 = 20/BC
⇒ BC = 20√3 m
∴ Distance between the foot of the light house to the ship = 20√3 m
Most Upvoted Answer
The height of a light house is 20 meters above sea level. The angle of...
To solve this problem, we can use trigonometry. Let's assume that the distance from the top of the lighthouse to the ship is "x" meters.
Since the angle of depression is 30 degrees, we can use the tangent function to find the value of "x". The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the lighthouse (20 meters) and the adjacent side is "x". Therefore, we have:
tan(30 degrees) = 20 / x
To find the value of "x", we can rearrange this equation:
x = 20 / tan(30 degrees)
Using a calculator, we can find that the tangent of 30 degrees is approximately 0.5774. Thus, we have:
x = 20 / 0.5774
x ≈ 34.64
Therefore, the distance from the top of the lighthouse to the ship in the sea is approximately 34.64 meters.
Since the angle of depression is 30 degrees, we can use the tangent function to find the value of "x". The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the lighthouse (20 meters) and the adjacent side is "x". Therefore, we have:
tan(30 degrees) = 20 / x
To find the value of "x", we can rearrange this equation:
x = 20 / tan(30 degrees)
Using a calculator, we can find that the tangent of 30 degrees is approximately 0.5774. Thus, we have:
x = 20 / 0.5774
x ≈ 34.64
Therefore, the distance from the top of the lighthouse to the ship in the sea is approximately 34.64 meters.
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The height of a light house is 20 meters above sea level. The angle of depression (from the top of the lighthouse) of a ship in the sea is 30°. What is the distance of the ship from the foot of the light house?a)16 mb)20√3 mc)20 md)30 mCorrect answer is option 'B'. Can you explain this answer?
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