Question

2) Match the correct answers.

You are the captain of the starship Selecsosi from the planet Yrtemoeg. While traveling in a
galaxy far, far away, you spotted a previously uncharted red dwarf star at a line of sight of 45°
from the ship (A). You needed to chart the new star, but you couldn't determine its distance
from the ship because the star was out of sensor range. After some quick thinking, you
remembered something you learned in Geometry that helped you figure out a way to find the
distance. As the ship continued on its course (AB), you kept watching the star until the line of
sight was exactly 90° from the ship (B). The distance you traveled from point A to point B was
125 million retemoliks. From this information, you were able to calculate the distance (BC) to
the star and chart its position.

Answer 1

In this scenario, you applied the principles of trigonometry, specifically the tangent function, to determine the distance to the uncharted red dwarf star. The angle at point A (45°) and the angle at point B (90°) allowed you to set up a right triangle with the star as the vertex. The line of sight from the ship to the star (AB) served as the opposite side, and the distance traveled by the ship (BC) acted as the adjacent side.

Using the tangent function:

`\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]`

In this case:

`\[ \tan(45°) = \frac{\text{AB}}{\text{BC}} \]`

Solving for BC:

`\[ BC = \frac{\text{AB}}{\tan(45°)} \]`

Given that AB is 125 million retemoliks, you could calculate BC, representing the distance to the star. This application of geometry and trigonometry allowed you to chart the position of the red dwarf star despite being out of sensor range.