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The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?
- a)45 m
- b)30 m
- c)103.8 m
- d)94.6 m
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The angle of elevation of the top of a lighthouse 60 m high, from two ...
Let BD be the lighthouse and A and C be the two points on ground.
Then, BD, the height of the lighthouse = 60 m
BAD = 45° , 
BCD = 60°
Distance between the two points A and C
= AC = BA + BC
= 60 + 34.6 [∵ Substituted value of BA and BC from (1) and (2)]
= 94.6 m
Most Upvoted Answer
The angle of elevation of the top of a lighthouse 60 m high, from two ...
Understanding the Problem
To find the distance between two points on the ground from which the angles of elevation to the top of a 60 m high lighthouse are 45° and 60°, we can use trigonometric relationships.
Key Trigonometric Relationships
1. For the point with a 45° angle of elevation:
- Let the distance from this point to the base of the lighthouse be D1.
- Using the tangent function:
- tan(45°) = height/base
- 1 = 60 / D1
- Therefore, D1 = 60 m.
2. For the point with a 60° angle of elevation:
- Let the distance from this point to the base of the lighthouse be D2.
- Using the tangent function:
- tan(60°) = height/base
- √3 = 60 / D2
- Therefore, D2 = 60 / √3 = 60 / 1.732 ≈ 34.64 m.
Calculating the Total Distance
The total distance between the two points (D) is the sum of D1 and D2:
- D = D1 + D2
- D = 60 m + 34.64 m ≈ 94.64 m.
Conclusion
Thus, the distance between the two points on the ground from which the angles of elevation are measured is approximately 94.6 m. Hence, the correct answer is option 'D'.
To find the distance between two points on the ground from which the angles of elevation to the top of a 60 m high lighthouse are 45° and 60°, we can use trigonometric relationships.
Key Trigonometric Relationships
1. For the point with a 45° angle of elevation:
- Let the distance from this point to the base of the lighthouse be D1.
- Using the tangent function:
- tan(45°) = height/base
- 1 = 60 / D1
- Therefore, D1 = 60 m.
2. For the point with a 60° angle of elevation:
- Let the distance from this point to the base of the lighthouse be D2.
- Using the tangent function:
- tan(60°) = height/base
- √3 = 60 / D2
- Therefore, D2 = 60 / √3 = 60 / 1.732 ≈ 34.64 m.
Calculating the Total Distance
The total distance between the two points (D) is the sum of D1 and D2:
- D = D1 + D2
- D = 60 m + 34.64 m ≈ 94.64 m.
Conclusion
Thus, the distance between the two points on the ground from which the angles of elevation are measured is approximately 94.6 m. Hence, the correct answer is option 'D'.
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The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?a)45 mb)30 mc)103.8 md)94.6 mCorrect answer is option 'D'. Can you explain this answer?
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