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The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex, then find the ratio of the height of pillar to the length of the shadow?
Verified Answer
The tangent of the angle of elevation of the top of the pillar is equa...
In right angle ΔABC, AB represents the vertical pole and BC represents the shadow on the ground.θ represents angle of elevation the sun.
tan θ = h / x
But length of shadow = height of the tower, i.e. h = x.
tan θ = h/ h = 1
tan θ = tan 45 theta
θ = 45 theta
Thus, angle of elevation of the sun = 45 theta
This question is part of UPSC exam. View all Class 10 courses
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The tangent of the angle of elevation of the top of the pillar is equa...
Problem:
The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex. Find the ratio of the height of the pillar to the length of the shadow.
Solution:
Let's assume the height of the pillar as 'h' and the length of the shadow as 's'.
Step 1: Understanding the Problem
We are given that the tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex. This means that the tangent of the angle of elevation, which is the ratio of the height of the pillar to the length of the shadow, is equal to 3/4.
Step 2: Writing the Equation
We can write the equation as follows:
tan(angle of elevation) = h / s = 3/4
Step 3: Solving the Equation
To find the ratio of the height of the pillar to the length of the shadow, we need to solve the equation for h/s.
Multiply both sides of the equation by s:
h = (3/4) * s
Step 4: Simplifying the Ratio
The ratio of the height of the pillar to the length of the shadow is h/s, which can be simplified as follows:
h/s = (3/4) * s / s
= 3/4
Step 5: Final Answer
The ratio of the height of the pillar to the length of the shadow is 3:4.
In conclusion, the height of the pillar is three-fourths of the length of its shadow at the vertex.
The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex. Find the ratio of the height of the pillar to the length of the shadow.
Solution:
Let's assume the height of the pillar as 'h' and the length of the shadow as 's'.
Step 1: Understanding the Problem
We are given that the tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex. This means that the tangent of the angle of elevation, which is the ratio of the height of the pillar to the length of the shadow, is equal to 3/4.
Step 2: Writing the Equation
We can write the equation as follows:
tan(angle of elevation) = h / s = 3/4
Step 3: Solving the Equation
To find the ratio of the height of the pillar to the length of the shadow, we need to solve the equation for h/s.
Multiply both sides of the equation by s:
h = (3/4) * s
Step 4: Simplifying the Ratio
The ratio of the height of the pillar to the length of the shadow is h/s, which can be simplified as follows:
h/s = (3/4) * s / s
= 3/4
Step 5: Final Answer
The ratio of the height of the pillar to the length of the shadow is 3:4.
In conclusion, the height of the pillar is three-fourths of the length of its shadow at the vertex.
Community Answer
The tangent of the angle of elevation of the top of the pillar is equa...
3 ratio ,4
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The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex, then find the ratio of the height of pillar to the length of the shadow?
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The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex, then find the ratio of the height of pillar to the length of the shadow? 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 The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex, then find the ratio of the height of pillar to the length of the shadow? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex, then find the ratio of the height of pillar to the length of the shadow?.
The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex, then find the ratio of the height of pillar to the length of the shadow? 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 The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex, then find the ratio of the height of pillar to the length of the shadow? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The tangent of the angle of elevation of the top of the pillar is equal to 3/4 of their shadow at the vertex, then find the ratio of the height of pillar to the length of the shadow?.
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