Answer:
4. Z ≈ 46.1°
5. T ≈ 45.2°
6. F ≈ 15.0°
Step-by-step explanation:
4.
We need to use the Law of Sines, which states that for a triangle with legnths a, b, and c and angles A, B, and C:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Here, we can say that ZY = a = 30, X = A = 110, XY = b = 23, and Z = B. Plug these in to find Z:
[tex]\frac{a}{sinA} =\frac{b}{sinB}[/tex]
[tex]\frac{30}{sin(110)} =\frac{23}{sinZ}[/tex]
Solve for Z:
Z ≈ 46.1°
5.
Use the Law of Sines as above.
[tex]\frac{a}{sinA} =\frac{b}{sinB}[/tex]
[tex]\frac{26}{sin(76)} =\frac{19}{sinT}[/tex]
Solve for T:
T ≈ 45.2°
6.
Again, use the Law of Sines as before.
[tex]\frac{a}{sinA} =\frac{b}{sinB}[/tex]
[tex]\frac{29}{sin(137)} =\frac{11}{sinF}[/tex]
Solve for F:
F ≈ 15.0°
