Step 1a

To find the lengths of sides XY and YZ in triangle XYZ, we can use the law of sines, which states:
\$"a"/("sin""A") = "b"/("sin""B") = "c"/("sin""C")\$

Given that angle X measures 48° and side XZ measures 16 units, we can find angle Z using the fact that the sum of angles in a triangle is 180°:
Z = 180 - ( X + Y)
Z = 180 - ( 48 + 64)
Z = 68°

Explanation: Here, introduce the law of sines formula and then find the angle Z value.

Step 1b

Now apply the law of sines to find the lengths of sides XY.

\$("XY")/("sin""X") = ("XZ")/("sin""Z")\$

\$("XY")/("sin"(48)) = 16/("sin"(68))\$

\$"XY" = (16 times "sin"(48))/("sin"(68))\$
XY = 12.81 units

Explanation: Here, use the law of sines rule for find the length of XY.

Step 1c

Now apply the law of sines to find the lengths of sides YZ.

\$("YZ")/("sin""Y") = ("XZ")/("sin""Z")\$

\$("YZ")/("sin"(64)) = 16/("sin"(68))\$

\$"YZ" = (16 times "sin"(64))/("sin"(68))\$

YZ = 15.5 units

So, the sides XY and YZ lengths are approximately 12.81 units and 15.5 units, respectively.

Explanation: Here also use the law of sines rule for find the length of YZ.