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In atriangle abc the triangles are in ap with common difference alpha such that cosalpha =21/22.if the triangle?
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In atriangle abc the triangles are in ap with common difference alpha ...
Triangle ABC in an Arithmetic Progression
Given that triangle ABC is an arithmetic progression (AP) with a common difference of alpha, we need to find the value of the triangle.
Step 1: Understanding the Problem
To solve this problem, we need to understand the concept of an arithmetic progression and how it relates to the angles of a triangle. We also need to know the value of cos(alpha) in order to find the triangle.
Step 2: What is an Arithmetic Progression?
An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the terms of the sequence represent the angles of the triangle.
Step 3: Finding the Common Difference
We are given that the common difference, alpha, is such that cos(alpha) = 21/22. To find the value of alpha, we can use the inverse cosine function:
alpha = arccos(21/22)
Step 4: Finding the Angles of the Triangle
Since triangle ABC is in an arithmetic progression, the angles can be represented as:
A = alpha
B = alpha + alpha = 2alpha
C = alpha + 2alpha = 3alpha
Step 5: Evaluating the Angles
Substituting the value of alpha, we can find the values of the angles:
A = arccos(21/22)
B = 2arccos(21/22)
C = 3arccos(21/22)
Step 6: Simplifying the Angles
We can simplify the expressions for the angles by using the trigonometric identity cos(3theta) = 4cos^3(theta) - 3cos(theta):
A = arccos(21/22)
B = 2arccos(21/22)
C = 3arccos(21/22) = arccos(21/22) + 2arccos(21/22)
Step 7: Simplifying Further
By substituting the value of alpha, we can simplify the expressions for the angles:
A = arccos(21/22)
B = 2arccos(21/22) = arccos(21/22) + arccos(21/22)
C = 3arccos(21/22) = arccos(21/22) + 2arccos(21/22)
Step 8: Evaluating the Angles
By substituting the value of cos(alpha), we can evaluate the expressions for the angles:
A = arccos(21/22) ≈ 0.446 rad
B = 2arccos(21/22) ≈ 0.892 rad
C = 3arccos(21/22) ≈ 1.338 rad
Step 9: Conclusion
Therefore, the angles of triangle ABC are approximately:
A ≈ 0.446 rad
B ≈ 0.892 rad
C ≈ 1.338 rad
Given that triangle ABC is an arithmetic progression (AP) with a common difference of alpha, we need to find the value of the triangle.
Step 1: Understanding the Problem
To solve this problem, we need to understand the concept of an arithmetic progression and how it relates to the angles of a triangle. We also need to know the value of cos(alpha) in order to find the triangle.
Step 2: What is an Arithmetic Progression?
An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the terms of the sequence represent the angles of the triangle.
Step 3: Finding the Common Difference
We are given that the common difference, alpha, is such that cos(alpha) = 21/22. To find the value of alpha, we can use the inverse cosine function:
alpha = arccos(21/22)
Step 4: Finding the Angles of the Triangle
Since triangle ABC is in an arithmetic progression, the angles can be represented as:
A = alpha
B = alpha + alpha = 2alpha
C = alpha + 2alpha = 3alpha
Step 5: Evaluating the Angles
Substituting the value of alpha, we can find the values of the angles:
A = arccos(21/22)
B = 2arccos(21/22)
C = 3arccos(21/22)
Step 6: Simplifying the Angles
We can simplify the expressions for the angles by using the trigonometric identity cos(3theta) = 4cos^3(theta) - 3cos(theta):
A = arccos(21/22)
B = 2arccos(21/22)
C = 3arccos(21/22) = arccos(21/22) + 2arccos(21/22)
Step 7: Simplifying Further
By substituting the value of alpha, we can simplify the expressions for the angles:
A = arccos(21/22)
B = 2arccos(21/22) = arccos(21/22) + arccos(21/22)
C = 3arccos(21/22) = arccos(21/22) + 2arccos(21/22)
Step 8: Evaluating the Angles
By substituting the value of cos(alpha), we can evaluate the expressions for the angles:
A = arccos(21/22) ≈ 0.446 rad
B = 2arccos(21/22) ≈ 0.892 rad
C = 3arccos(21/22) ≈ 1.338 rad
Step 9: Conclusion
Therefore, the angles of triangle ABC are approximately:
A ≈ 0.446 rad
B ≈ 0.892 rad
C ≈ 1.338 rad
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In atriangle abc the triangles are in ap with common difference alpha such that cosalpha =21/22.if the triangle?
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In atriangle abc the triangles are in ap with common difference alpha such that cosalpha =21/22.if the triangle? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about In atriangle abc the triangles are in ap with common difference alpha such that cosalpha =21/22.if the triangle? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In atriangle abc the triangles are in ap with common difference alpha such that cosalpha =21/22.if the triangle?.
In atriangle abc the triangles are in ap with common difference alpha such that cosalpha =21/22.if the triangle? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about In atriangle abc the triangles are in ap with common difference alpha such that cosalpha =21/22.if the triangle? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In atriangle abc the triangles are in ap with common difference alpha such that cosalpha =21/22.if the triangle?.
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