Answer:
Step-by-step explanation:
1). In ΔABC,
For angle A as a reference angle,
Opposite side of ∠A → BC
Adjacent side of ∠A → AC
Hypotenuse → AB
2). By using tangent ratio in ΔYWZ,
tan(72°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(72°) = [tex]\frac{12}{x}[/tex]
x = [tex]\frac{12}{\text{tan}(72)}[/tex]
x = 3.899
x ≈ 3.9
3). By using sine rule in ΔKNM,
tan(x°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
tan(x) = [tex]\frac{20}{58}[/tex]
x = [tex]\text{tan}^{-1}(\frac{20}{58} )[/tex]
x = 19.03
x ≈ 19.0°
4). By applying cosine ratio in ΔJKF,
tan(70°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(70) = [tex]\frac{60}{x}[/tex]
x = [tex]\frac{60}{\text{tan}(70)}[/tex]
x = 21.838
x ≈ 21.8
