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From the top of a 40 ft tall building, the angle of depression to the base of a tower is 60 degree and the angle of elevation to the top of the tower is 30 degree. Find the height of the tower.?
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From the top of a 40 ft tall building, the angle of depression to the ...
- **Given Information**:
Given a 40 ft tall building with an angle of depression of 60 degrees to the base of a tower and an angle of elevation of 30 degrees to the top of the tower.
- **Finding the Height of the Tower**:
To find the height of the tower, we need to set up a right triangle using the information given. Let's denote the height of the tower as 'h'.
- **Using Trigonometry**:
From the information given, we can see that we have two right triangles formed - one using the building, the tower, and the base of the tower, and the other using the building, the tower, and the top of the tower.
- **Calculating the Height of the Tower**:
First, we need to find the distance from the building to the base of the tower. Using trigonometry, we can calculate this distance as 40/tan(60) = 40/√3 = 40√3 ft.
Next, we can find the total height of the tower by adding the height of the building (40 ft) to the height from the base of the tower to the top of the tower. Using trigonometry again, we can calculate this height as h = (40√3)tan(30) = 40√3(1/√3) = 40 ft.
- **Conclusion**:
Therefore, the height of the tower is 40 ft.
Given a 40 ft tall building with an angle of depression of 60 degrees to the base of a tower and an angle of elevation of 30 degrees to the top of the tower.
- **Finding the Height of the Tower**:
To find the height of the tower, we need to set up a right triangle using the information given. Let's denote the height of the tower as 'h'.
- **Using Trigonometry**:
From the information given, we can see that we have two right triangles formed - one using the building, the tower, and the base of the tower, and the other using the building, the tower, and the top of the tower.
- **Calculating the Height of the Tower**:
First, we need to find the distance from the building to the base of the tower. Using trigonometry, we can calculate this distance as 40/tan(60) = 40/√3 = 40√3 ft.
Next, we can find the total height of the tower by adding the height of the building (40 ft) to the height from the base of the tower to the top of the tower. Using trigonometry again, we can calculate this height as h = (40√3)tan(30) = 40√3(1/√3) = 40 ft.
- **Conclusion**:
Therefore, the height of the tower is 40 ft.
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From the top of a 40 ft tall building, the angle of depression to the base of a tower is 60 degree and the angle of elevation to the top of the tower is 30 degree. Find the height of the tower.?
Question Description
From the top of a 40 ft tall building, the angle of depression to the base of a tower is 60 degree and the angle of elevation to the top of the tower is 30 degree. Find the height of the tower.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about From the top of a 40 ft tall building, the angle of depression to the base of a tower is 60 degree and the angle of elevation to the top of the tower is 30 degree. Find the height of the tower.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the top of a 40 ft tall building, the angle of depression to the base of a tower is 60 degree and the angle of elevation to the top of the tower is 30 degree. Find the height of the tower.?.
From the top of a 40 ft tall building, the angle of depression to the base of a tower is 60 degree and the angle of elevation to the top of the tower is 30 degree. Find the height of the tower.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about From the top of a 40 ft tall building, the angle of depression to the base of a tower is 60 degree and the angle of elevation to the top of the tower is 30 degree. Find the height of the tower.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the top of a 40 ft tall building, the angle of depression to the base of a tower is 60 degree and the angle of elevation to the top of the tower is 30 degree. Find the height of the tower.?.
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