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A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel?
Most Upvoted Answer
A TV tower stands vertically on a bank of canal . from a point on the ...
Given information:
- The angle of elevation of the top of the tower from a point directly opposite the tower is 60 degrees.
- From another point 20m away from the first point, on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30 degrees.
Let's solve this problem step by step:
Step 1: Drawing a diagram
First, let's draw a diagram to visualize the given information.
```
T
/|
/ |
/ | h
/ |
/ |
D / |
| / |
| / |
| / |
| / |
|/ |
P-----------O
20m
```
- T: Top of the tower
- D: Foot of the tower
- P: First point on the other bank directly opposite the tower
- O: Second point, 20m away from point P on the line joining P to D
Step 2: Identifying the right-angled triangles
From the diagram, we can identify two right-angled triangles:
- Triangle TOP: This triangle has the top of the tower as the top vertex, the foot of the tower as the bottom vertex, and the line joining P to D as the hypotenuse.
- Triangle POD: This triangle has point P as the top vertex, the foot of the tower as the bottom vertex, and point O as the right-angle vertex.
Step 3: Solving for the height of the tower
In triangle TOP, we can use trigonometry to find the height of the tower (h).
- In triangle TOP, the angle of elevation of the top of the tower from point P is 60 degrees. Therefore, the angle between the hypotenuse and the base is 90 - 60 = 30 degrees.
- We can use the tangent function to find h. tan(30) = h / 20m.
- Rearranging the equation, h = 20m * tan(30).
Step 4: Solving for the width of the canal
In triangle POD, we can use trigonometry to find the width of the canal (x).
- In triangle POD, the angle of elevation of the top of the tower from point P is 30 degrees. Therefore, the angle between the base and the hypotenuse is 90 - 30 = 60 degrees.
- We can use the cosine function to find x. cos(60) = x / 20m.
- Rearranging the equation, x = 20m * cos(60).
Step 5: Calculating the values
Using a scientific calculator, we can calculate the values of h and x:
- h = 20m * tan(30) ≈ 20m * 0.577 ≈ 11.54m
- x = 20m * cos(60) ≈ 20m * 0.5 ≈ 10m
Step 6: Final answer
The height of the tower is approximately 11.54m and the width of the canal is approximately 10m.
- The angle of elevation of the top of the tower from a point directly opposite the tower is 60 degrees.
- From another point 20m away from the first point, on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30 degrees.
Let's solve this problem step by step:
Step 1: Drawing a diagram
First, let's draw a diagram to visualize the given information.
```
T
/|
/ |
/ | h
/ |
/ |
D / |
| / |
| / |
| / |
| / |
|/ |
P-----------O
20m
```
- T: Top of the tower
- D: Foot of the tower
- P: First point on the other bank directly opposite the tower
- O: Second point, 20m away from point P on the line joining P to D
Step 2: Identifying the right-angled triangles
From the diagram, we can identify two right-angled triangles:
- Triangle TOP: This triangle has the top of the tower as the top vertex, the foot of the tower as the bottom vertex, and the line joining P to D as the hypotenuse.
- Triangle POD: This triangle has point P as the top vertex, the foot of the tower as the bottom vertex, and point O as the right-angle vertex.
Step 3: Solving for the height of the tower
In triangle TOP, we can use trigonometry to find the height of the tower (h).
- In triangle TOP, the angle of elevation of the top of the tower from point P is 60 degrees. Therefore, the angle between the hypotenuse and the base is 90 - 60 = 30 degrees.
- We can use the tangent function to find h. tan(30) = h / 20m.
- Rearranging the equation, h = 20m * tan(30).
Step 4: Solving for the width of the canal
In triangle POD, we can use trigonometry to find the width of the canal (x).
- In triangle POD, the angle of elevation of the top of the tower from point P is 30 degrees. Therefore, the angle between the base and the hypotenuse is 90 - 30 = 60 degrees.
- We can use the cosine function to find x. cos(60) = x / 20m.
- Rearranging the equation, x = 20m * cos(60).
Step 5: Calculating the values
Using a scientific calculator, we can calculate the values of h and x:
- h = 20m * tan(30) ≈ 20m * 0.577 ≈ 11.54m
- x = 20m * cos(60) ≈ 20m * 0.5 ≈ 10m
Step 6: Final answer
The height of the tower is approximately 11.54m and the width of the canal is approximately 10m.
Community Answer
A TV tower stands vertically on a bank of canal . from a point on the ...
Is this from rd sharma
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A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel?
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A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel? 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 TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel?.
A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel? 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 TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel?.
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A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel?, a detailed solution for A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel? has been provided alongside types of A TV tower stands vertically on a bank of canal . from a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60* from another point 20m away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30*. find the height of the tower and the width of the canel? theory, EduRev gives you an
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