Final Answer:
a) Measure of angle XYZ = 90 degrees
b) Measure of angle YXZ = 71 degrees
c) Side YZ = 15 units
d) Side MN = 15 units
Explanation:
The given problem involves a right-angled triangle XYZ with the side XZ measuring 19 units. From the equation XYZ = MNL, it's evident that angle XYZ equals 90 degrees due to the presence of a right angle in a triangle. Therefore, the measure of angle XYZ is 90 degrees.
To determine the other angle and side lengths, trigonometric ratios can be applied. By using trigonometric functions such as sine, cosine, or tangent, the remaining angles and sides can be calculated. Utilizing the sine function, the angle YXZ is found to be approximately 71 degrees.
Additionally, to find the remaining side lengths, the Pythagorean theorem can be employed since it applies to right-angled triangles. Knowing XZ = 19 and angle XYZ = 90 degrees, it allows us to solve for side YZ. The calculation results in YZ measuring 15 units.
Similarly, as the sides of the triangles XYZ and MNL are corresponding, side MN can be deduced to be equal to side YZ, measuring 15 units.
In summary, the triangle XYZ has angle measures of 90 degrees (XYZ) and approximately 71 degrees (YXZ), with side lengths of 19 units (XZ) and 15 units (YZ), while side MN, corresponding to YZ, also measures 15 units.