00:01
So in this problem we're told that the distance from the sun to earth, sun to earth, this distance which i labeled b, is equal to 149 ,600 ,000 kilometers.
00:17
The distance from the sun to venus, this distance here a, is equal to 108 ,200 ,000 kilometers.
00:29
And then the angle between the line of sight from earth to the sun and the line of sight from earth to venus, this angle here alpha, is equal to 10.
00:45
And then we want to use this information to find the possible distances between earth and venus, which is this distance here c, earth to venus.
01:05
So here we're given two sides and one angle.
01:10
That means we can use the law of sines to solve this problem.
01:17
And the law of sines tells us that sine alpha over a is equal to sine beta over b is equal to sine gamma over c.
01:30
And then here beta will be opposite of side b and gamma will be opposite of side c.
01:38
So then using the information we have, we can start plugging this in the formula.
01:47
We have sine alpha, we have a and b.
01:52
So we want to find beta first.
01:54
Beta is equal to the inverse sine of b divided by a times sine of alpha, which is just rewriting this piece right here.
02:14
And then take the inverse sine to solve for beta.
02:20
So when we plug in all our information, it gives us that beta is equal to inverse sine of b over a.
02:30
Let's get rid of all the zeros because they cancel out.
02:34
We just get 1496 over 1082 sine alpha is 10 degrees.
02:43
So this then is equal to 13 .89 degrees, which is our first possible solution, solution one...