Solve the Right Triangle $0.314$ Arc Seconds (Parallax Is the Change in Position of the Angles

question 141

Multiple Choice

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-In 1838 , the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at $0.314$ arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about $150,000,000 \mathrm {~km}$ and $\theta = 0.314$ seconds $= \frac { 0.314 } { 60 }$ minutes $= \frac { 0.314 } { 60 \cdot 60 }$ degrees, determine the distance $\mathrm { d }$ from Earth to 61 Cygni using Bessel's figures. Express the answer in scienti notation.

• A) \(9.85 \times 10 ^ { 13 } \mathrm {~km}\)
• B) \(1.05 \times 10 ^ { 14 } \mathrm {~km}\)
• C) \(2.28 \times 10 ^ { 13 } \mathrm {~km}\)
• D) \(1.97 \times 10 ^ { 14 } \mathrm {~km}\)

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Definitions:

Simple Linear Regression

Simple linear regression is a method for predicting a quantitative outcome using a single explanatory variable, based on the linear relationship between them.

Least Squares

A method in statistics for approximating the solution of overdetermined systems, by minimizing the differences between the observed and predicted values.

Simple Linear Regression

A statistical method used to model the relationship between a single independent variable and a dependent variable by fitting a linear equation to observed data.

Normally Distributed

A statistical distribution that is symmetrical about the mean, where most observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions.