Answer:
21) x = 22.9, y = 38.4
22) x = 14.0, y = 98.0
Explanation:
Question 21
As the interior angles of a triangle sum to 180°, the measure of the third angle of the given triangle is 100°.

As we know all interior angles and the length of one side of the triangle, we can use the Law of Sines to find the the values of x and y.

From inspection of the given triangle:
- Angle 28° is opposite the side labelled x.
- Angle 52° is opposite the side labelled y.
- Angle 100° is opposite the side labelled 48.
Substitute these values into the Law of Sines formula:

Solve for x:




Solve for y:




Therefore, the values of x and y (rounded to the nearest tenth) are:

Question 22
As we know the lengths of two sides of the triangle and their included angle, we can use the Cosine Rule to find the measure of side x.

From inspection of the given triangle:
Substitute these values into the Cosine Rule and solve for x:





Now use the Law of Sines to calculate angle y.
As angle y is obtuse, and the sine of an obtuse angle is the same as the sine of its supplement, then:

Rearrange the equation to isolate y:



Substitute the found value of x and evaluate:




Therefore, the values of x and y (rounded to the nearest tenth) are: