Question

\Triangle X Y Z is shown. Angle X Z Y is 63 degrees. The length of X Z is 2.7 and the length of X Y is 2.8.

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 approximate measure of angle Y? Use the law of sines to find the answer.

52°
59°
64°
67°

Answer 1

To find the measure of angle Y in triangle XYZ, you can use the law of sines. By setting up a proportion and solving for sine(angle Y), you can then find the angle itself by taking the inverse sine. In this case, angle Y is approximately 59°.

Step-by-step explanation:

In this problem, we are given a triangle XYZ with angle XZY measuring 63 degrees, a length of XZ equal to 2.7, and a length of XY equal to 2.8. To find the measure of angle Y, we can use the law of sines. The law of sines states that the ratio of the sine of an angle to the length of the side opposite that angle is equal for all angles in a triangle. Using the law of sines, we can set up the following proportion:

Substituting the given values, we have:

Cross-multiplying and solving for sine(angle Y), we get

Finally, we can find angle Y by taking the inverse sine of both sides:

Calculating this expression, we find that angle Y is approximately