Need help with this review question. More explanation and how far is the star from the sun in astronomical units? Also how do I write an expression to calculate d for any of the…

Question

asked May 27, 2023 157k views

1 Answer

Joe Brunscheon · Answer 1 · 2023-05-30T14:30:36+0000

To solve this problem, we will use the trigonometric function tangent. Recall that by definition in a right triangle:

$\tan \theta=\frac{opposite\text{ leg}}{\text{adjacent leg}}\text{.}$

In the given diagram, opposite leg=1 A.U. ( astronomical unit), θ=0.00001389°, and adjacent leg =d, therefore:

$\tan (0.00001389)=(1)/(d)\text{.}$

Solving the above equation for d, we get:

$d=\frac{1A.U\text{.}}{\text{tan(}0.00001389)}\text{.}$

Simplifying, we get:

$d=4124966.128\text{ A.U.}$

Answer:

$d=4124966.128\text{ A.U.}$

For any star, if we are given an angle θ, we can use the following expression to determine its distance from the Sun:

$d=\frac{1A.U\text{.}}{\tan\theta}$