Question

Triangle X Y Z is shown. Angle X Y Z is 75 degrees and angle Y Z X is 50 degrees. The length of X Y is 2 and the length of Y Z is x.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

Which is the best approximation of the value of x? Use the law of sines to find the answer.

1.5 units
2.1 units
2.9 units
3.6 units

Answer 1

The third angle of the triangle will be 60°. The nearest value of x is 2.1 units. Then the correct option is B.

What is the law of sines?

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

$\rm \dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}$

Triangle XYZ is shown.

Angle XYZ is 75 degrees and angle YZX is 50 degrees.

The length of XY is 2 and the length of YZ is x.

Then the third angle of the triangle will be

⇒ 180° - 50° - 70°

⇒60°

Then we have

x / sin 60° = 2 / sin 50°

x = 2.26

Then the nearest value of x is 2.1 units.

Then the correct option is B.

Learn more about the law of sines here:

brainly.com/question/17289163

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