SOLUTION: i have a triangle with three angles of 45 75 and 60 degrees. the side opposite the 45 degrees is 5 long. how do i achieve the other two side please help. thank you

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Question 288597: i have a triangle with three angles of 45 75 and 60 degrees. the side opposite the 45 degrees is 5 long. how do i achieve the other two side please help. thank you
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Let your angles be A,B,C.

Let the sides opposite each of those angles be a,b,c.

Side a is opposite angle A.
Side b is opposite angle B.
Side c is opposite angle C.

angle A is equal to 45 degrees.
angle B is equal to 75 degrees.
angle C is equal to 60 degrees.

You are given that the side opposite the 45 degree angle is 5 units long.

Side a is 5 units long.

The law of Sines states that:

a%2Fsin%28A%29+=+b%2Fsin%28B%29+=+c%2Fsin%28C%29

This means that the length of each side of a triangle is proportional to the measure of its corresponding angle.

In your triangle, this equation becomes:



5%2F.707106781 = 7.071067812

The ratio of b%2F.965925826 should be equal to 7.071067812 which means that b = .965925826+%2A+7.071067812 which equals 6.830127019.

The ratio of c%2F.866025404 should be equal to 7.071067812 which means that c = .866025404+%2A+7.071067812 which equals 6.123724357.

The sides of your triangle should be:

a = 5
b = 6.830127019
c = 6.123724357

The law of sines ratio should hold.

That ratio is, once again:

a%2Fsin%28A%29+=+b%2Fsin%28B%29+=+c%2Fsin%28c%29.

In your equation, that becomes:

5%2Fsin%2845%29+=+6.830127019%2Fsin%2875%29+=+6.123724357%2Fsin%2860%29.

Using the sines of those angles previously calculated gets us

7.071067812+=+7.071067812+=+7.071067812

The law of sines has held and your answer is:

a = 5
b = 6.830127019
c = 6.123724357