Question

Astronomers often measure large distances using astronomical units (AL) where 1 AU is the average distance from Earth to the Sun. In the image, adrepresents the distance from a star to the Sun. Using a technique called *stellar parallax,* astronomers determined © is 0.00001272 degrees.

Answer 1

Step 1:

Apply the right angle trigonometric ratio to find the distance of the star from the sun.

Step 2:

Given data

$\begin{gathered} \theta\text{ = }0.00001272 \\ \text{Opposite = 1} \\ \text{Adjacent = d} \end{gathered}$

1)

$\begin{gathered} tan\theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \tan \text{ 0.00001272 = }\frac{1}{d} \\ 0.000000222005\text{ = }\frac{1}{d} \\ d\text{ = }\frac{1}{0.000000222005} \\ d\text{ = 4504385.182 AU} \end{gathered}$

2)

The expression is

$\begin{gathered} \text{tan}(0.00001272)\text{ = }\frac{1}{d} \\ or \\ \text{tan(}\theta)\text{ = }\frac{1}{d} \end{gathered}$