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From the top of a vertical tower the angle of depression of two cars in the same straight line with the base of the tower at an instant are found to be 45*and 60*if the cars are 100mapart and are on the same side of the tower find the hieght of the tower?
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From the top of a vertical tower the angle of depression of two cars i...
Given:
- Angle of depression of car 1 = 45°
- Angle of depression of car 2 = 60°
- Distance between the two cars = 100m
To find:
- Height of the tower
Assumptions:
- The ground is flat and horizontal.
- The cars are on the same side of the tower.
Approach:
1. Draw a diagram to visualize the problem.
2. Use trigonometry to form equations based on the given angles and distances.
3. Solve the equations to find the height of the tower.
Diagram:
```
A
|\
| \
| \
h | \ d
| \
| \
| \
| \
B-------C
|-----|
100m
```
In the diagram, A represents the top of the tower, B and C represent the positions of the two cars, and d represents the height of the tower.
Equations:
1. In triangle ABC, tan(45°) = h / d
2. In triangle ABC, tan(60°) = (h + 100) / d
Solution:
1. From equation 1, we get h = d * tan(45°)
2. From equation 2, we get h + 100 = d * tan(60°)
3. Substitute the value of h from equation 1 into equation 2:
d * tan(45°) + 100 = d * tan(60°)
4. Simplify the equation:
d * 1 + 100 = d * (√3)
d + 100 = d√3
5. Rearrange the equation to isolate d:
d√3 - d = 100
d (√3 - 1) = 100
d = 100 / (√3 - 1)
6. Use a calculator to find the value of d:
d ≈ 239.6m
7. Substitute the value of d into equation 1 to find h:
h = d * tan(45°)
h ≈ 239.6m * 1
h ≈ 239.6m
Answer:
The height of the tower is approximately 239.6 meters.
- Angle of depression of car 1 = 45°
- Angle of depression of car 2 = 60°
- Distance between the two cars = 100m
To find:
- Height of the tower
Assumptions:
- The ground is flat and horizontal.
- The cars are on the same side of the tower.
Approach:
1. Draw a diagram to visualize the problem.
2. Use trigonometry to form equations based on the given angles and distances.
3. Solve the equations to find the height of the tower.
Diagram:
```
A
|\
| \
| \
h | \ d
| \
| \
| \
| \
B-------C
|-----|
100m
```
In the diagram, A represents the top of the tower, B and C represent the positions of the two cars, and d represents the height of the tower.
Equations:
1. In triangle ABC, tan(45°) = h / d
2. In triangle ABC, tan(60°) = (h + 100) / d
Solution:
1. From equation 1, we get h = d * tan(45°)
2. From equation 2, we get h + 100 = d * tan(60°)
3. Substitute the value of h from equation 1 into equation 2:
d * tan(45°) + 100 = d * tan(60°)
4. Simplify the equation:
d * 1 + 100 = d * (√3)
d + 100 = d√3
5. Rearrange the equation to isolate d:
d√3 - d = 100
d (√3 - 1) = 100
d = 100 / (√3 - 1)
6. Use a calculator to find the value of d:
d ≈ 239.6m
7. Substitute the value of d into equation 1 to find h:
h = d * tan(45°)
h ≈ 239.6m * 1
h ≈ 239.6m
Answer:
The height of the tower is approximately 239.6 meters.
Community Answer
From the top of a vertical tower the angle of depression of two cars i...
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From the top of a vertical tower the angle of depression of two cars in the same straight line with the base of the tower at an instant are found to be 45*and 60*if the cars are 100mapart and are on the same side of the tower find the hieght of the tower?
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From the top of a vertical tower the angle of depression of two cars in the same straight line with the base of the tower at an instant are found to be 45*and 60*if the cars are 100mapart and are on the same side of the tower find the hieght of the tower? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about From the top of a vertical tower the angle of depression of two cars in the same straight line with the base of the tower at an instant are found to be 45*and 60*if the cars are 100mapart and are on the same side of the tower find the hieght of the tower? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the top of a vertical tower the angle of depression of two cars in the same straight line with the base of the tower at an instant are found to be 45*and 60*if the cars are 100mapart and are on the same side of the tower find the hieght of the tower?.
From the top of a vertical tower the angle of depression of two cars in the same straight line with the base of the tower at an instant are found to be 45*and 60*if the cars are 100mapart and are on the same side of the tower find the hieght of the tower? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about From the top of a vertical tower the angle of depression of two cars in the same straight line with the base of the tower at an instant are found to be 45*and 60*if the cars are 100mapart and are on the same side of the tower find the hieght of the tower? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the top of a vertical tower the angle of depression of two cars in the same straight line with the base of the tower at an instant are found to be 45*and 60*if the cars are 100mapart and are on the same side of the tower find the hieght of the tower?.
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