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A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building?
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A statue 1.6 m tall,stands on the top of a pedestal. From a point on t...
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A statue 1.6 m tall,stands on the top of a pedestal. From a point on t...
**Problem:**
A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees, and from the same point, the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building?
**Solution:**
To solve this problem, we can use trigonometry and the concept of similar triangles.
Let's assume the height of the building (including the statue and pedestal) is 'h' meters.
Let's break down the problem step by step:
1. **Identify the triangles:**
We have two triangles in this problem:
- Triangle ABC: This triangle represents the entire building (including the statue and pedestal).
- Triangle ADE: This triangle represents just the statue and pedestal.
2. **Identify the given angles and side lengths:**
- The angle of elevation of the top of the statue from point D is 60 degrees.
- The angle of elevation of the top of the pedestal from point D is 45 degrees.
- The height of the statue (side DE) is 1.6 meters.
3. **Find the height of the building:**
To find the height of the building, we need to find the length of side AD in Triangle ABC.
- Let's consider the right-angled triangle ADE.
- In triangle ADE, we have the angle of elevation of the statue as 60 degrees.
- Therefore, the angle ADE is also 60 degrees.
- We know the height of the statue (side DE) is 1.6 meters.
- Using trigonometry, we can find the length of side AE:
- tan(60) = DE / AE
- tan(60) = 1.6 / AE
- AE = 1.6 / tan(60)
- AE = 1.6 / √3
- AE = 1.6 * √3 / 3
- Now, let's consider the right-angled triangle ABC.
- In triangle ABC, we have the angle of elevation of the pedestal as 45 degrees.
- Therefore, the angle ABC is also 45 degrees.
- We know the length of side AE is 1.6 * √3 / 3 (as calculated above).
- Using trigonometry, we can find the length of side AD:
- tan(45) = AE / AD
- tan(45) = (1.6 * √3 / 3) / AD
- 1 = (1.6 * √3 / 3) / AD
- AD = (1.6 * √3 / 3)
Hence, the height of the building (including the statue and pedestal) is approximately 1.6 * √3 / 3 meters.
A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees, and from the same point, the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building?
**Solution:**
To solve this problem, we can use trigonometry and the concept of similar triangles.
Let's assume the height of the building (including the statue and pedestal) is 'h' meters.
Let's break down the problem step by step:
1. **Identify the triangles:**
We have two triangles in this problem:
- Triangle ABC: This triangle represents the entire building (including the statue and pedestal).
- Triangle ADE: This triangle represents just the statue and pedestal.
2. **Identify the given angles and side lengths:**
- The angle of elevation of the top of the statue from point D is 60 degrees.
- The angle of elevation of the top of the pedestal from point D is 45 degrees.
- The height of the statue (side DE) is 1.6 meters.
3. **Find the height of the building:**
To find the height of the building, we need to find the length of side AD in Triangle ABC.
- Let's consider the right-angled triangle ADE.
- In triangle ADE, we have the angle of elevation of the statue as 60 degrees.
- Therefore, the angle ADE is also 60 degrees.
- We know the height of the statue (side DE) is 1.6 meters.
- Using trigonometry, we can find the length of side AE:
- tan(60) = DE / AE
- tan(60) = 1.6 / AE
- AE = 1.6 / tan(60)
- AE = 1.6 / √3
- AE = 1.6 * √3 / 3
- Now, let's consider the right-angled triangle ABC.
- In triangle ABC, we have the angle of elevation of the pedestal as 45 degrees.
- Therefore, the angle ABC is also 45 degrees.
- We know the length of side AE is 1.6 * √3 / 3 (as calculated above).
- Using trigonometry, we can find the length of side AD:
- tan(45) = AE / AD
- tan(45) = (1.6 * √3 / 3) / AD
- 1 = (1.6 * √3 / 3) / AD
- AD = (1.6 * √3 / 3)
Hence, the height of the building (including the statue and pedestal) is approximately 1.6 * √3 / 3 meters.
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A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building?
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A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building? 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 statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building?.
A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building? 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 statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building?.
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A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building?, a detailed solution for A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building? has been provided alongside types of A statue 1.6 m tall,stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point of the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the building? theory, EduRev gives you an
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