86.9k views
3 votes
Two planets are orbiting a star. Planet B can be seen from Planet A with the eye, but as the figure shows, Planet could be located at either of two possible positions. Planet A is 65 million miles from the star and Planet B is 45 million miles from the star, as shown in the figure below. If the viewing angle between the star and Planet B is 19 , find the possible distances from Planet A to Planet B . Round your answers to the nearest tenth.

1 Answer

4 votes

Answer:

Explanation:

Let's call the distance from Planet A to one of the possible positions of Planet B "x". We can use trigonometry to relate the angle between the star and Planet B (19°), the distance from the star to Planet A (65 million miles), and the distances from Planet A to Planet B (x).

In a right triangle with angle 19°, the opposite side is x and the adjacent side is 65 - 45 = 20 million miles. Therefore, we can use the tangent function to relate these sides:

tan(19°) = x / 20

Solving for x, we get:

x = 20 tan(19°) ≈ 6.7 million miles

So one possible distance from Planet A to Planet B is approximately 6.7 million miles.

However, there is another possible position for Planet B, which is on the other side of Planet A as shown in the figure. In this case, the distance from Planet A to Planet B is:

y = 65 + 45 + 20 = 130 million miles

Therefore, the two possible distances from Planet A to Planet B are approximately 6.7 million miles and 130 million miles (rounded to the nearest tenth).

User Jayesh Doolani
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories