XYZ is an isosceles triangle with /XY/=/XZ/=6cm and Y ANGLE X Z=120 degree. Calculate the length of YZ
Since XYZ is an isosceles triangle, we know that the lengths XY and XZ are equal. Given that XY and XZ both have lengths of 6cm, we can denote the length of YZ as y cm.
Given the angle YXZ is 120 degrees, we know that the sum of the angles in a triangle is always 180 degrees. Therefore, angle XYZ and angle ZXY are equal and sum up to 180 - 120 = 60 degrees.
In an isosceles triangle, the two equal angles are opposite the two equal sides. Therefore, angle ZXY and angle XYZ are equal.
Using this information, we can determine that each of the angles XYZ and ZXY is 60/2 = 30 degrees.
Now, we can use the law of sines to find y (the length of YZ):
sin(XYZ)/6 = sin(30)/y
sin(30) is equal to 0.5, so the equation becomes:
sin(XYZ)/6 = 0.5/y
Cross multiplying, we get:
y * sin(XYZ) = 6 * 0.5
Simplifying, we find:
y * sin(XYZ) = 3
Since sin(XYZ) is always less than or equal to 1, the maximum value of y is y = 3.
Therefore, the length of YZ is 3 cm.