Answer:
[tex]a=8 ,b=6 ,c=35 ,d=37 ,e=15 ,f=17 ,x=32 ,y=65 ,z=25[/tex]
Step-by-step explanation:
[tex]Sin(x)=\frac{opposite side}{hypotenuse} \\Cos(x)=\frac{adjacent side}{hypotenuse} \\Tan(x)=\frac{opposite side}{adjacent side}[/tex]
x is in degrees.
14.
[tex]Sin(37)=\frac{b}{10} \\\\b=10Sin(37)=6\\\\Cos(37)=\frac{a}{10}\\ a=10Cos(37)=8[/tex]
15.
[tex]Cos(71)=\frac{12}{d}\\ d=12Sec(71)=36.858641...\\Tan(71)=\frac{c}{12} \\c=12Tan(71)=34.85053056..[/tex]
16.
[tex]Tan(28)=\frac{8}{e} \\e=8Cot(28)=15.04581176..\\Sin(28)=\frac{8}{f} \\f=8Cosec(28)=17.04043576..[/tex]
17.
[tex]Tanx=\frac{28}{45}\\ x=Tan^-(\frac{28}{45})=31.89079...\\[/tex]
18.
[tex]Cos(y)=\frac{77}{85} \\y=Cos^-(\frac{77}{85})=25.05761..\\ z=90-y=64.94239...[/tex]
