Using the law of sines, it is found that the inequality that relates KL and YZ in the triangles is: KL > YZ.
What is the law of sines?
Suppose we have a triangle in which:
- The length of the side opposite to angle A is a.
- The length of the side opposite to angle B is b.
- The length of the side opposite to angle C is c.
The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
For these problems, we have that:
- Size YZ is opposite to the angle of 30º.
- Size KL is opposite to the angle of 45º.
Hence:
sin(30º)/YZ = sin(45º)/KL
KLsin(30º)/YZ = sin(45º)
KL/YZ = sin(45º)/sin(30º)
Since sin(45º) > sin(30º), the inequality is:
KL > YZ.
More can be learned about the law of sines at https://brainly.com/question/25535771
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