An alien on a distant planet realizes that using trigonometry and the distance to one of its moons it is possible to calculate the distance to the nearby sun.

Question

An alien on a distant planet realizes that using trigonometry and the distance to one of its moons it is possible to calculate the distance to the nearby sun.

Let O be the center of the planet, and let A be the center of the moon.

The alien begins with the premise that, during a half moon, the moon forms a right triangle with the Sun and the planet. The the alien observes that the angle between the Sun and Moon is ϕ=89.55ϕ=89.55 degrees.

If the distance to the moon is about 224000 km, estimate the distance from the planet to the sun using these values. Round to the nearest 1000 km.

Answer 1

have distance to moon from sun d_ms= 224000/cos(89.5)

d_ms is the hypotenuse

distance to planet from sun d_ps=d_ms*sin(89.55)

you really do need to draw and label a diagram