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Use the law of sines to find the value of y. round to the nearest tenth. law of sines: startfraction sine (uppercase a) over a endfraction = startfraction sine (uppercase b) over b endfraction = startfraction sine (uppercase c) over c endfraction 1.4 units 1.6 units 2.5 units 2.6 units

Sagot :

Using the law of sine on the given triangle, we get the measure of y as given by: Option C: 2.5 units

What is law of sines?

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

we have, by law of sines,

[tex]\dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b} = \dfrac{\sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

For this case, the missing image is attached below.

Applying the sine law, as we have:

  • The side opposite to angle Y is XZ of length y units,
  • The side opposite to the angle Z is XY of length 2 units,
  • The side opposite to the angle X is YZ

The first two angles Y and Z are enough. (we use angle Z as the length of the side opposite to Z is known).

Using sine law, we get:

[tex]\dfrac{\sin(m\angle Y)}{y} = \dfrac{\sin(m\angle Z)}{2}\\\\y = \dfrac{\sin(75^\circ) \times 2}{\sin(50^\circ)} \approx 2.522 \approx 2.5 \: \rm units[/tex]

Thus, using the law of sine on the given triangle, we get the measure of y as given by: Option C: 2.5 units

Learn more about law of sines here:

https://brainly.com/question/17289163

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