Answer:
Step-by-step explanation:
1). From the triangle given in the figure,
m∠BAD = 26°
By applying tangent rule in ΔADB,
tan(∠BAD) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(26°) = [tex]\frac{BD}{AD}[/tex]
BD = 21[tan(26°)]
BD = 10.24
By applying sine rule in ΔBDC,
sin(52°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(52°) = [tex]\frac{10.24}{x}[/tex]
x = [tex]\frac{10.24}{\text{sin}(52)}[/tex]
x = 12.99
x ≈ 13.0 units
2). By applying cosine rule in ΔADB,
cos(39°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(39°) = [tex]\frac{BD}{50}[/tex]
BD = 50cos(39°)
BD = 38.86
By applying sine rule in ΔBDC,
sin(24°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(24°) = [tex]\frac{38.86}{x}[/tex]
x = [tex]\frac{38.86}{\text{sin(24)}}[/tex]
x = 95.54
x ≈ 95.5 units
