Answer:
86.3
Explanation:
To find the two possible values of x, we can use the law of sines, which states that:
asinA=bsinB=csinC
where A, B, and C are the angles of the triangle and a, b, and c are the opposite sides.
In this case, we are given A = 50°, a = 10 cm, and b = 9 cm. We can use the law of sines to find sin B:
10sin50°=9sinB
sinB=109sin50°≈0.6904
Now, we can use the inverse sine function to find B:
B=sin−1(0.6904)≈43.7°
However, this is not the only possible value for B. Since the sine function is positive in both quadrant I and quadrant II, there is another angle with the same sine value but in quadrant II. This angle is the supplement of B:
B′=180°−B≈180°−43.7°=136.3°
This means that there are two possible triangles that satisfy the given information: one with B = 43.7° and one with B = 136.3°.
To find x, we need to find C for each triangle using the fact that the sum of angles in a triangle is 180°:
C=180°−A−B≈180°−50°−43.7°=86.3°
C′=180°−A−B′≈180°−50°−136.3°=−6.3°
However, C’ is not a valid angle for a triangle because it is negative. Therefore, we can ignore this possibility and conclude that there is only one possible value for x:
x=C≈86.3°