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The three angles of a triangle were measured with the following results: A = 42°05', B = 115°38', and C = 22°08'. Determine the most probable value of each angle. %3D

The three angles of a triangle were measured with the following results: A = 42°05', B = 115°38', and C = 22°08'. Determine the most probable value of each angle. %3D

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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1. The three angles of a triangle were measured with the following results: A = 42°05', B = 115°38', and C = 22°08'. Determine the most probable value of each angle. 2. The angles about a point have the following observed values: 87°07'50", 125°17'20", and 147°35'20". Determine the most probable value of the three angles. 3. The interior angles of a quadrilateral were observed to be: A = 100°35'40", B = 118°44'15", C = 80°54'35", and D = 59°45'50". Determine the most probable value of each of these angles. 4. A quantity was measured ten times with the following results: 34.630, 34.626, 34.364, 34.628, 34.629, 34.626, 34.627, 34.633, 34.625, and 34.624 meters. Determine the probable error of the mean and the relative precision of the mean. 5. A surveying instructor sent all the 40 students in his class out to measure a distance between two points marked on a runway. The students working in groups of four came up with 10 different measurements as follows: 920.45, 921.05, 921.65, 920.25, 920.15, 921.85, 921.95, 920.45, 921.15, and 921.35 meters. Assuming these values are equally reliable and that variations result only from accidental errors, determine the relative precision of single measurement and the relative precision of the mean. 6. The following values were determined in a series of rod readings made under identical conditions: 3.312, 3.307, 3.304, 3.306, 3.309, 3.301, 3.311, 3.308, 3.312, 3.306, and 3.313 meters. Determine the following: most probable value of the observed rod readings, probable error of a single measurement and of the mean, and the relative precision of a single measurement and of the mean.
Transcribed Image Text:1. The three angles of a triangle were measured with the following results: A = 42°05', B = 115°38', and C = 22°08'. Determine the most probable value of each angle. 2. The angles about a point have the following observed values: 87°07'50", 125°17'20", and 147°35'20". Determine the most probable value of the three angles. 3. The interior angles of a quadrilateral were observed to be: A = 100°35'40", B = 118°44'15", C = 80°54'35", and D = 59°45'50". Determine the most probable value of each of these angles. 4. A quantity was measured ten times with the following results: 34.630, 34.626, 34.364, 34.628, 34.629, 34.626, 34.627, 34.633, 34.625, and 34.624 meters. Determine the probable error of the mean and the relative precision of the mean. 5. A surveying instructor sent all the 40 students in his class out to measure a distance between two points marked on a runway. The students working in groups of four came up with 10 different measurements as follows: 920.45, 921.05, 921.65, 920.25, 920.15, 921.85, 921.95, 920.45, 921.15, and 921.35 meters. Assuming these values are equally reliable and that variations result only from accidental errors, determine the relative precision of single measurement and the relative precision of the mean. 6. The following values were determined in a series of rod readings made under identical conditions: 3.312, 3.307, 3.304, 3.306, 3.309, 3.301, 3.311, 3.308, 3.312, 3.306, and 3.313 meters. Determine the following: most probable value of the observed rod readings, probable error of a single measurement and of the mean, and the relative precision of a single measurement and of the mean.
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