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From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is: (SSC Sub. Ins. 2015)
- a)16
- b)12
- c)15
- d)18
Correct answer is option 'D'. Can you explain this answer?
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From two points on the ground and lying on a straight line through the...
To solve this problem, we can use the concept of trigonometry and complementary angles.
Given:
- Two points on the ground lying on a straight line through the foot of a pillar.
- The two angles of elevation of the top of the pillar from these two points are complementary to each other.
- The distances of the two points from the foot of the pillar are 12 meters and 27 meters.
- The two points lie on the same side of the pillar.
Let's denote the height of the pillar as 'h' meters.
- Angle of Elevation:
The angle of elevation is the angle formed between the line of sight and the horizontal line. In this case, the line of sight is from the two points on the ground to the top of the pillar.
- Complementary Angles:
Complementary angles are two angles that add up to 90 degrees. In this case, the two angles of elevation are complementary to each other.
- Using Trigonometry:
We can use the tangent function to relate the angles of elevation to the height of the pillar.
Let's consider the first point, which is 12 meters away from the foot of the pillar.
- Tangent of the angle of elevation from the first point:
tan(angle1) = h/12
Now, let's consider the second point, which is 27 meters away from the foot of the pillar.
- Tangent of the angle of elevation from the second point:
tan(angle2) = h/27
Since the two angles of elevation are complementary, we can write:
angle1 + angle2 = 90 degrees
- Applying the Tan Rule:
Using the tangent addition formula, we can write:
tan(angle1 + angle2) = (tan(angle1) + tan(angle2)) / (1 - tan(angle1) * tan(angle2))
Substituting the values we have:
tan(90) = (h/12 + h/27) / (1 - h/12 * h/27)
Since tan(90) is undefined, we can rewrite the equation as:
1/0 = (h/12 + h/27) / (1 - h/12 * h/27)
Simplifying the equation, we get:
0 = (27h + 12h) / (12 * 27 - h^2)
0 = 39h / (324 - h^2)
- Solving for h:
Since the numerator is zero (0), we can solve for the denominator:
324 - h^2 = 0
h^2 = 324
Taking the square root of both sides, we get:
h = ±18
Since the height cannot be negative, we take the positive value:
h = 18 meters
Therefore, the height of the pillar is 18 meters. Thus, the correct answer is option 'D'.
Given:
- Two points on the ground lying on a straight line through the foot of a pillar.
- The two angles of elevation of the top of the pillar from these two points are complementary to each other.
- The distances of the two points from the foot of the pillar are 12 meters and 27 meters.
- The two points lie on the same side of the pillar.
Let's denote the height of the pillar as 'h' meters.
- Angle of Elevation:
The angle of elevation is the angle formed between the line of sight and the horizontal line. In this case, the line of sight is from the two points on the ground to the top of the pillar.
- Complementary Angles:
Complementary angles are two angles that add up to 90 degrees. In this case, the two angles of elevation are complementary to each other.
- Using Trigonometry:
We can use the tangent function to relate the angles of elevation to the height of the pillar.
Let's consider the first point, which is 12 meters away from the foot of the pillar.
- Tangent of the angle of elevation from the first point:
tan(angle1) = h/12
Now, let's consider the second point, which is 27 meters away from the foot of the pillar.
- Tangent of the angle of elevation from the second point:
tan(angle2) = h/27
Since the two angles of elevation are complementary, we can write:
angle1 + angle2 = 90 degrees
- Applying the Tan Rule:
Using the tangent addition formula, we can write:
tan(angle1 + angle2) = (tan(angle1) + tan(angle2)) / (1 - tan(angle1) * tan(angle2))
Substituting the values we have:
tan(90) = (h/12 + h/27) / (1 - h/12 * h/27)
Since tan(90) is undefined, we can rewrite the equation as:
1/0 = (h/12 + h/27) / (1 - h/12 * h/27)
Simplifying the equation, we get:
0 = (27h + 12h) / (12 * 27 - h^2)
0 = 39h / (324 - h^2)
- Solving for h:
Since the numerator is zero (0), we can solve for the denominator:
324 - h^2 = 0
h^2 = 324
Taking the square root of both sides, we get:
h = ±18
Since the height cannot be negative, we take the positive value:
h = 18 meters
Therefore, the height of the pillar is 18 meters. Thus, the correct answer is option 'D'.
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From two points on the ground and lying on a straight line through the...
Let height of the pillar is h m
In ΔACD
In ΔABD
In ΔACD
In ΔABD
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From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is: (SSC Sub. Ins. 2015)a)16b)12c)15d)18Correct answer is option 'D'. Can you explain this answer?
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From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is: (SSC Sub. Ins. 2015)a)16b)12c)15d)18Correct answer is option 'D'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is: (SSC Sub. Ins. 2015)a)16b)12c)15d)18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is: (SSC Sub. Ins. 2015)a)16b)12c)15d)18Correct answer is option 'D'. Can you explain this answer?.
From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is: (SSC Sub. Ins. 2015)a)16b)12c)15d)18Correct answer is option 'D'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is: (SSC Sub. Ins. 2015)a)16b)12c)15d)18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is: (SSC Sub. Ins. 2015)a)16b)12c)15d)18Correct answer is option 'D'. Can you explain this answer?.
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