Question 1126582: Find all solutions to the following triangle. (Round your answers for the angles B, C, B', and C' to the nearest whole number. Round your answers for the sides c and c' to one decimal place. If either triangle is not possible, enter NONE in each corresponding answer blank.)
A = 65°, b = 6.7 yd, a = 6.2 yd
First triangle (assume B ≤ 90°):
B= °
C= °
c = yd
Second triangle (assume B' > 90°):
B'= °
C'= °
c'= yd
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
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.
I find it easiest always to draw the figure in the same orientation: unknown side horizontal, with the given angle at the left.
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.
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.
The required calculations are then....
(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.
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