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The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.?
Most Upvoted Answer
The line joining the top of a hill to the foot of the hill makes angle...
Given information:
- The line joining the top of the hill to the foot of the hill makes an angle of 30 degrees with the horizontal through the foot of the hill.
- The tops of the temple and the guest house both make an elevation of 45 degrees at the foot of the hill.
- The guest house is 100 m away from the foot of the hill along the hill.
To find:
- The heights of the guest house and the temple.
Step-by-step solution:
1. Setting up the diagram:
Let's first set up the diagram to visualize the given information.
We have a hill, with the guest house located halfway between the foot of the hill and the top. The line joining the top of the hill to the foot of the hill makes an angle of 30 degrees with the horizontal through the foot of the hill. The tops of the temple and guest house both make an elevation of 45 degrees at the foot of the hill.
We can label the foot of the hill as point A, the guest house as point B, and the top of the hill as point C.
Now, let's draw the diagram:
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C (Top of the hill)
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A B (Guest house)
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2. Finding the height of the guest house:
We know that the angle of elevation from the foot of the hill to the guest house is 45 degrees. Since we have the distance from the foot of the hill to the guest house, we can use trigonometry to find the height of the guest house.
Let's consider triangle ABC, where AB represents the distance from the foot of the hill to the guest house and BC represents the height of the guest house.
Using trigonometry, we have:
tan(45 degrees) = BC / AB
Since tan(45 degrees) = 1, we can simplify the equation to:
1 = BC / AB
Therefore, BC = AB.
Since the distance from the foot of the hill to the guest house is given as 100 m, the height of the guest house is also 100 m.
3. Finding the height of the temple:
To find the height of the temple, we need to use the information that the tops of the temple and guest house both make an elevation of 45 degrees at the foot of the hill.
Let's consider triangle ABC, where AC represents the height of the temple.
Using trigonometry, we have:
tan(45 degrees) = AC / AB
Since tan(45 degrees) = 1, we can simplify the equation to:
1 = AC / AB
Therefore, AC = AB.
Since the height of the guest house is 100 m, the height of the temple is also 100 m.
Answer:
The height of the guest house is 100 m and the height of the temple is also 100 m.
- The line joining the top of the hill to the foot of the hill makes an angle of 30 degrees with the horizontal through the foot of the hill.
- The tops of the temple and the guest house both make an elevation of 45 degrees at the foot of the hill.
- The guest house is 100 m away from the foot of the hill along the hill.
To find:
- The heights of the guest house and the temple.
Step-by-step solution:
1. Setting up the diagram:
Let's first set up the diagram to visualize the given information.
We have a hill, with the guest house located halfway between the foot of the hill and the top. The line joining the top of the hill to the foot of the hill makes an angle of 30 degrees with the horizontal through the foot of the hill. The tops of the temple and guest house both make an elevation of 45 degrees at the foot of the hill.
We can label the foot of the hill as point A, the guest house as point B, and the top of the hill as point C.
Now, let's draw the diagram:
```
C (Top of the hill)
|
|\
| \
| \
| \
| \
| \
| \
-----------------
A B (Guest house)
```
2. Finding the height of the guest house:
We know that the angle of elevation from the foot of the hill to the guest house is 45 degrees. Since we have the distance from the foot of the hill to the guest house, we can use trigonometry to find the height of the guest house.
Let's consider triangle ABC, where AB represents the distance from the foot of the hill to the guest house and BC represents the height of the guest house.
Using trigonometry, we have:
tan(45 degrees) = BC / AB
Since tan(45 degrees) = 1, we can simplify the equation to:
1 = BC / AB
Therefore, BC = AB.
Since the distance from the foot of the hill to the guest house is given as 100 m, the height of the guest house is also 100 m.
3. Finding the height of the temple:
To find the height of the temple, we need to use the information that the tops of the temple and guest house both make an elevation of 45 degrees at the foot of the hill.
Let's consider triangle ABC, where AC represents the height of the temple.
Using trigonometry, we have:
tan(45 degrees) = AC / AB
Since tan(45 degrees) = 1, we can simplify the equation to:
1 = AC / AB
Therefore, AC = AB.
Since the height of the guest house is 100 m, the height of the temple is also 100 m.
Answer:
The height of the guest house is 100 m and the height of the temple is also 100 m.
Community Answer
The line joining the top of a hill to the foot of the hill makes angle...
The height of quest house is 41 m and the height of temple is 82 m.
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The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.?
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The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.? 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 The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.?.
The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.? 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 The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.?.
Solutions for The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.? in English & in Hindi are available as part of our courses for Class 10.
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The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.?, a detailed solution for The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.? has been provided alongside types of The line joining the top of a hill to the foot of the hill makes angle of 30 degree with the horizontal through the foot of the hill .There is one Temple at the top of the hill and a guest house half way from the foot of the top. The tops of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest houses is 100 m away from the foot of the hills along the hill ,find the heights of the guest house and the temple.? theory, EduRev gives you an
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