# Help me with this one please

## Answers

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!

Answer:Sin F = 0.7534Cos F = 0.6575Tan F= 1.145Step-by-step explanation:From the given figure we can see that,triangle DEF is right angled triangleBase = DF = 48Hypotenuse = EF = 73Height = ED To find EDWe have ,Hypotenuse² = Base² + Height²EF² = DF² + ED²ED² = EF² - DF² = 73² - 482ED² = 3025ED = √3025 = 55To find Sin (F)Sin ∅ =Opposite side /HypotenuseSin F = ED/EF = 55/73 = 0.7534To find Sin (F)Cos ∅ =Adjacent side /HypotenuseCos F =DF/EF = 48/73 = 0.6575To find Sin (F)Tan ∅ =Opposite side /Adjacent side Tan F = ED/DF = 55/48 = 1.145