An astronomer knows the distances from herself to stars AAA and BBB, as well as the distance between them. The distances are 450450450, 400400400, and 909090 light years (\text{l. Y.}l. Y.Start text, l, point, y, point, end text) respectively. If the astronomer's telescope is currently pointed at star AAA, how many degrees must she rotate her telescope to see star BBB?

She must rotate her telescope 10.27°

Step-by-step explanation:

The distances are in light-years:

The distance between the astronomer and planet A is:

aA = 450 ly

the distance between the astronomer and planet B is:

aB = 400 Ly

and the distance between both planets is

AB = 90 Ly

then we have the length of 3 sides of a triangle, we want to find the angle that is opposite of the side AB.

using the rule of the cosines we have that:

Cos(a) = (aA^2 + aB^2 + AB^2)/(2*aA*aB)

cos(a) = (450^2 + 400^2 - 90^2)/(2*400*450) = 0.984

a = arcos(0.984) = 10.27°

10

Step-by-step explanation:

You have to round 10.27 to nearest ten which is 10.