Question 1126582
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In this kind of problem, you are always given one angle and the length of the side opposite that angle, plus the length of one of the two other sides.<br>
I find it easiest always to draw the figure in the same orientation: unknown side horizontal, with the given angle at the left.<br>
So in this problem the horizontal base is AB, with the 65 degree angle A at the left.  Side b slants up to the right from A to C; side a slants down from C to B.<br>
The height of the triangle (vertical distance from C to side AB) is b*sinA() = 6.7*sin(65) = 6.07.  Since side a is greater than 6.07 and less than 6.7, there will be two triangles.<br>
The required calculations are then....<br>
(1) Find the measure of the acute angle B using the law of sines.
(2) By symmetry, the obtuse angle B will be 180 degrees minus the acute angle B.
(3) Find angle C of each triangle using the angle sum of 180 degrees for a triangle.
(4) Find the lengths of side c in each triangle using the law of sines.