Question

Help me with this one please

Answer 1

Sin F = 0.7534

Cos F = 0.6575

Tan F= 1.145

Explanation:

From the given figure we can see that,

triangle DEF is right angled triangle

Base = DF = 48

Hypotenuse = EF = 73

Height = ED

To find ED

We have ,

Hypotenuse² = Base² + Height²

EF² = DF² + ED²

ED² = EF² - DF² = 73² - 482

ED² = 3025

ED = √3025 = 55

To find Sin (F)

Sin ∅ =Opposite side /Hypotenuse

Sin F = ED/EF = 55/73 = 0.7534

To find Sin (F)

Cos ∅ =Adjacent side /Hypotenuse

Cos F =DF/EF = 48/73 = 0.6575

To find Sin (F)

Tan ∅ =Opposite side /Adjacent side

Tan F = ED/DF = 55/48 = 1.145

Answer 2

Hello!

The answer is:

`sin(F)=(OppositeSide)/(Hypotenuse)=(55)/(73)=0.75`

`cos(F)=(AdjacentSide)/(Hypotenuse)=(48)/(73)=0.66\\\\tan(F)=(OppositeSide)/(AdjacentSide)=(55)/(48)=1.15`

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:

`c^(2)=a^(2) +b^(2)`

Where:

`c=hypotenuse=73\\a=AdjacentSide=48\\b=OppositeSide`

So, the opposite side will be:

`OppositeSide=\sqrt{c^(2)-a^(2)}=\sqrt{73^(2)-48^(2)}=√(5329-2304) \\OppositeSide=√(3025)=55`

Then:

`sin(F)=(OppositeSide)/(Hypotenuse)=(55)/(73)=0.75`

`cos(F)=(AdjacentSide)/(Hypotenuse)=(48)/(73)=0.66\\\\tan(F)=(OppositeSide)/(AdjacentSide)=(55)/(48)=1.15`

Have a nice day!