In triangle XYZ, angle X is 100°, angle Y is 30°, and angle Z is 50°. Side XZ is 6.3 cm. Side XY is 9.C5 cm.
What do you want to find in the question?
If you're trying to find the 3rd side, use law of sines, or law of cosines.
sinZ/XY = sinX/YZ.
sin50/9.5 = sin100/YZ,
YZ *sin50 = 9.5*sin100,
YZ = 9.5*sin100/sin50 =
To find the length of side YZ in triangle XYZ, we can use the sine rule. The sine rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
Let's label the lengths of the sides as follows:
Side XZ = a = 6.3 cm
Side XY = b = 9.5 cm
Side YZ = c (which is what we want to find)
Next, we need to find the measure of angle ZYX. We can use the fact that the sum of angles in a triangle is 180 degrees:
angle ZYX = 180 - 100 - 30 = 50 degrees
Using the sine rule:
a / sin(A) = b / sin(B) = c / sin(C)
Plugging in the values we know:
6.3 / sin(100) = 9.5 / sin(30) = c / sin(50)
Next, we can solve for c:
c = sin(50) * (6.3 / sin(100))
c = sin(50) * (9.5 / sin(30))
Now let's calculate side YZ using these values:
c = 0.766 * (6.3 / 0.985)
c = 0.766 * 6.384
Therefore, side YZ is approximately 4.89 cm.