Question

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

The total distance to the red dwarf star (AC) is also 125 million retemoliks, as it forms a right-angled triangle.

As the captain of the starship Selecsosi, you realized that you could use trigonometry to calculate the distance to the uncharted red dwarf star. The key insight comes from the fact that you formed a right triangle with the star as the vertex angle, with sides labeled as follows:

AB: The distance traveled by the ship, given as 125 million retemoliks.

AC: The unknown distance to the red dwarf star.

BC: The distance from the star to the line of sight when it formed a right angle with the ship's course.

Since you observed the star at two different points (A and B) and you know the angle at A is 45° and the angle at B is 90°, you can use trigonometric ratios to find the distances.

Let's use the tangent function:

tan(45∘ )= AB/BC

​You know AB (125 million retemoliks) and can solve for

BC. The tangent of 45 degrees is 1.

BC=AB×tan(45∘ )

BC=125 million retemoliks×1

BC=125 million retemoliks

So, the distance from the red dwarf star to the line of sight (BC) is 125 million retemoliks. Therefore, the total distance to the red dwarf star (AC) is also 125 million retemoliks, as it forms a right-angled triangle.