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A tower stands vertically on the ground from a point on the ground which is 25 m away from the foot of tower if the height of tower is 25√3 metres find the angle of elevation.
- a)60°
- b)30°
- c)120°
- d)90°
Correct answer is option 'A'. Can you explain this answer?
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Given Data:
- Distance from the foot of the tower to the point on the ground: 25 m
- Height of the tower: 25√3 m
Calculating Angle of Elevation:
1. Let the angle of elevation be θ.
2. We have a right-angled triangle formed by the tower, the ground, and the line of sight.
3. The opposite side to the angle of elevation is the height of the tower (25√3 m).
4. The adjacent side is the distance from the foot of the tower to the point on the ground (25 m).
5. Using the tangent function: tan(θ) = opposite/adjacent.
6. Plugging in the values: tan(θ) = (25√3)/25.
7. Simplifying: tan(θ) = √3.
8. To find the angle θ, we need to find the angle whose tangent is √3.
9. The angle whose tangent is √3 is 60°.
10. Therefore, the angle of elevation is 60°.
Therefore, the correct answer is option A) 60°.
- Distance from the foot of the tower to the point on the ground: 25 m
- Height of the tower: 25√3 m
Calculating Angle of Elevation:
1. Let the angle of elevation be θ.
2. We have a right-angled triangle formed by the tower, the ground, and the line of sight.
3. The opposite side to the angle of elevation is the height of the tower (25√3 m).
4. The adjacent side is the distance from the foot of the tower to the point on the ground (25 m).
5. Using the tangent function: tan(θ) = opposite/adjacent.
6. Plugging in the values: tan(θ) = (25√3)/25.
7. Simplifying: tan(θ) = √3.
8. To find the angle θ, we need to find the angle whose tangent is √3.
9. The angle whose tangent is √3 is 60°.
10. Therefore, the angle of elevation is 60°.
Therefore, the correct answer is option A) 60°.
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