A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/4$ . If side C has a length of $9$ and the angle between sides B and C is $( 3 pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2016-05-24T15:14:23

$A=B=11.791$ to 3 decimal places

Particularly so in geometry it is a good idea to do a rough sketch so that you can see what is happening:

Tony B

Known: Sum of the internal angles of a triangle is 180 degrees

$=> /_AC = pi( 1-1/4 - 3/8) = (3pi)/8 -> 67 1/2 color(white)()^0$

Using the sine rule $->9/(sin(pi/4))=B/(sin((3pi)/8))= A/(sin((3pi)/8 ))$

$=> A=B = (9sin((3pi)/8))/(sin(pi/4))=11.791$ to 3 decimal places

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/4(pi)/4. If side C has a length of 9 9 and the angle between sides B and C is ( 3 pi)/8( 3 pi)/8, what are the lengths of sides A and B?