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What is the difference between the sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface?
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What is the difference between the sum of interior angles of plane tri...
Difference between sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface
Plane Triangle
- A plane triangle is a three-sided polygon with all three sides and angles lying on a plane.
- The sum of the interior angles of a plane triangle is always 180 degrees.
- The area of a plane triangle can be calculated using the formula: A = 1/2 * base * height.
Spherical Triangle
- A spherical triangle is a three-sided polygon with all three sides and angles lying on the surface of a sphere.
- The sum of the interior angles of a spherical triangle is always greater than 180 degrees.
- The area of a spherical triangle can be calculated using the formula: A = R^2 * ((A1 + A2 + A3) - pi), where R is the radius of the sphere and A1, A2, and A3 are the measures of the angles of the spherical triangle.
Calculation
- Given that the area of the triangle is 195 sq. kilometers on the Earth's surface.
- We need to determine whether the triangle is a plane triangle or a spherical triangle.
- If the triangle is a plane triangle, then the sum of the interior angles would be 180 degrees.
- If the triangle is a spherical triangle, then the sum of the interior angles would be greater than 180 degrees.
- Since the triangle is on the surface of the Earth, we can assume that it is a spherical triangle.
- Using the formula for the area of a spherical triangle, we can solve for the sum of the interior angles:
A = R^2 * ((A1 + A2 + A3) - pi)
195 sq. km = R^2 * ((A1 + A2 + A3) - pi)
Assuming the radius of the Earth to be 6371 km,
195 sq. km = 6371^2 * ((A1 + A2 + A3) - pi)
(A1 + A2 + A3) - pi = 195 sq. km / (6371^2)
(A1 + A2 + A3) - pi = 4.84 x 10^-6
(A1 + A2 + A3) = pi + 4.84 x 10^-6
Therefore, the sum of the interior angles of the spherical triangle is pi + 4.84 x 10^-6 radians, which is greater than 180 degrees.
Conclusion
- The difference between the sum of the interior angles of a plane triangle and a spherical triangle for an area of 195 sq. kilometers on the Earth's surface is that the sum of the interior angles of a spherical triangle is greater than 180 degrees, while the sum of the interior angles of a plane triangle is always 180 degrees.
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What is the difference between the sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface?
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What is the difference between the sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about What is the difference between the sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the difference between the sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface?.
What is the difference between the sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about What is the difference between the sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the difference between the sum of interior angles of plane triangle and spherical triangle for area of triangle 195 sq. kilometer on the Earth's surface?.
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