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In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ?
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In some building especially in industries the roof is inclined this in...
Application of Trigonometry in Inclined Roofs
Given Information:
- The roof of the industry is inclined at angles alpha and beta with the horizontal line.
- The value of cosec alpha is √2.
- The value of cot beta is 1.
- Both alpha and beta are acute angles.
Solution:
Drawing:
First, draw a rough diagram of the inclined roof with the given angles α and β as shown below:
Trigonometric Functions:
We know that:
- cosec α = 1/sin α
- cot β = 1/tan β
Using the Given Information:
From the given information, we have:
- cosec α = √2
- cot β = 1
Finding sin α and sin β:
We can find sin α using the value of cosec α:
- cosec α = 1/sin α
- √2 = 1/sin α
- sin α = 1/√2 = √2/2
We can find sin β using the value of cot β:
- cot β = 1/tan β
- 1 = cos β/sin β
- sin β = cos β/1 = cos β
Finding sin (α + β):
Using the formula for sin (α + β), we get:
- sin (α + β) = sin α cos β + cos α sin β
- sin (α + β) = (√2/2) * 1 + (1/√2) * cos α
Finding cos α:
To find cos α, we can use the identity:
- sin² α + cos² α = 1
Solving for cos α, we get:
- sin² α + cos² α = 1
- (√2/2)² + cos² α = 1
- 1/2 + cos² α = 1
- cos² α = 1/2
- cos α = ±√(1/2)
Since alpha is an acute angle, cos α is positive. Therefore, cos α = √(1/2) = √2/2.
Substituting Values:
Substituting the values of sin α, cos α, and sin β into the formula for sin (α + β), we get:
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In some building especially in industries the roof is inclined this in...
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In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ?
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In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ? 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 In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ?.
In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ? 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 In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ?.
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In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ?, a detailed solution for In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ? has been provided alongside types of In some building especially in industries the roof is inclined this inclination of roof is the application of trigonometry functions here the roof of the industry is inclined at angles alpha and beta with horizontal line as shown determine the value of sin Alpha beta ifcosecalpha=√2 and cot=1 where both alpha and beta are acute angle ? theory, EduRev gives you an
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