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Solve the Right Triangle 0.3140.314 Arc Seconds (Parallax Is the Change in Position of the Angles

Question 275

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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 0.3140.314 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 km150,000,000 \mathrm {~km} and θ=0.314\theta = 0.314 seconds =0.31460= \frac { 0.314 } { 60 } minutes =0.3146060= \frac { 0.314 } { 60 \cdot 60 } degrees, determine the distance d\mathrm { d } from Earth to 61 Cygni using Bessel's figures. Express the answer in scienti notation.
 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}


A) 9.85×1013 km9.85 \times 10 ^ { 13 } \mathrm {~km}
B) 1.05×1014 km1.05 \times 10 ^ { 14 } \mathrm {~km}
C) 2.28×1013 km2.28 \times 10 ^ { 13 } \mathrm {~km}
D) 1.97×1014 km1.97 \times 10 ^ { 14 } \mathrm {~km}

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