Hello!
The answer is:
[tex]sin(F)=\frac{OppositeSide}{Hypotenuse}=\frac{55}{73}=0.75[/tex]
[tex]cos(F)=\frac{AdjacentSide}{Hypotenuse}=\frac{48}{73}=0.66\\\\tan(F)=\frac{OppositeSide}{AdjacentSide}=\frac{55}{48}=1.15[/tex]
Why?
Since we are working with a right triangle, we can use the Pythagorean Theorem to know the missing side size (Opposite Side).
Pythagorean Theorem formula:
[tex]c^{2}=a^{2} +b^{2}[/tex]
Where:
[tex]c=hypotenuse=73\\a=AdjacentSide=48\\b=OppositeSide[/tex]
So, the opposite side will be:
[tex]OppositeSide=\sqrt{c^{2}-a^{2}}=\sqrt{73^{2}-48^{2}}=\sqrt{5329-2304} \\OppositeSide=\sqrt{3025}=55[/tex]
Then:
[tex]sin(F)=\frac{OppositeSide}{Hypotenuse}=\frac{55}{73}=0.75[/tex]
[tex]cos(F)=\frac{AdjacentSide}{Hypotenuse}=\frac{48}{73}=0.66\\\\tan(F)=\frac{OppositeSide}{AdjacentSide}=\frac{55}{48}=1.15[/tex]
Have a nice day!
