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A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)?
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A tree stands vertically on a hill side which makes an angle of 15degr...
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A tree stands vertically on a hill side which makes an angle of 15degr...
Given:
- The angle between the tree and the horizontal is 15 degrees.
- The angle of elevation from a point on the ground to the top of the tree is 60 degrees.
- The distance from the base of the tree to the point on the ground is 35 meters.
To find:
- The height of the tree.
Approach:
1. Draw a diagram to visualize the given information.
2. Split the diagram into two right-angled triangles: one with the top of the tree as the vertex and the other with the bottom of the tree as the vertex.
3. Use trigonometric ratios to set up equations based on the angles and sides of the triangles.
4. Solve the equations simultaneously to find the height of the tree.
Diagram:
```
/|
/ |
/ |
/ θ | x
/ |
/________|
T D G
- T represents the top of the tree.
- D represents the point on the ground.
- G represents the base of the tree.
- θ represents the angle of elevation.
- x represents the height of the tree.
```
Solution:
1. From the diagram, we can see that tan(θ) = x / DG.
2. tan(θ) can be written as tan(60) = x / DG.
3. tan(60) is equal to the square root of 3.
4. Therefore, we have √3 = x / DG.
Calculating DG:
1. From the diagram, we can see that tan(15) = x / GD.
2. tan(15) can be written as tan(15) = x / GD.
3. We know that tan(15) is approximately 0.26795.
4. Therefore, we have 0.26795 = x / GD.
Solving the Equations:
1. Rearrange the equation DG = x / √3 to isolate DG.
DG = x / √3.
2. Substitute the value of DG from the previous equation into the equation 0.26795 = x / GD.
0.26795 = x / (x / √3).
0.26795 = √3.
3. Cross-multiply to solve for x.
x = 0.26795 * √3.
x ≈ 0.4641.
Final Answer:
The height of the tree is approximately 0.4641 meters, which can be rounded to 35√2 meters.
- The angle between the tree and the horizontal is 15 degrees.
- The angle of elevation from a point on the ground to the top of the tree is 60 degrees.
- The distance from the base of the tree to the point on the ground is 35 meters.
To find:
- The height of the tree.
Approach:
1. Draw a diagram to visualize the given information.
2. Split the diagram into two right-angled triangles: one with the top of the tree as the vertex and the other with the bottom of the tree as the vertex.
3. Use trigonometric ratios to set up equations based on the angles and sides of the triangles.
4. Solve the equations simultaneously to find the height of the tree.
Diagram:
```
/|
/ |
/ |
/ θ | x
/ |
/________|
T D G
- T represents the top of the tree.
- D represents the point on the ground.
- G represents the base of the tree.
- θ represents the angle of elevation.
- x represents the height of the tree.
```
Solution:
1. From the diagram, we can see that tan(θ) = x / DG.
2. tan(θ) can be written as tan(60) = x / DG.
3. tan(60) is equal to the square root of 3.
4. Therefore, we have √3 = x / DG.
Calculating DG:
1. From the diagram, we can see that tan(15) = x / GD.
2. tan(15) can be written as tan(15) = x / GD.
3. We know that tan(15) is approximately 0.26795.
4. Therefore, we have 0.26795 = x / GD.
Solving the Equations:
1. Rearrange the equation DG = x / √3 to isolate DG.
DG = x / √3.
2. Substitute the value of DG from the previous equation into the equation 0.26795 = x / GD.
0.26795 = x / (x / √3).
0.26795 = √3.
3. Cross-multiply to solve for x.
x = 0.26795 * √3.
x ≈ 0.4641.
Final Answer:
The height of the tree is approximately 0.4641 meters, which can be rounded to 35√2 meters.
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A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)?
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A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)? 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 A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)?.
A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)? 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 A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)?.
Solutions for A tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. From a point on the ground 35 m down the hill from the base of the tree. The angle of elevation of the top of the tree is 60 degree. Find the height of the tree.?(answer is 35 underroot 2 m)? in English & in Hindi are available as part of our courses for Class 10.
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