Question

Help me with this one please

Answer 1

Hello!

The answer is:

$sin(F)=\frac{OppositeSide}{Hypotenuse}=\frac{55}{73}=0.75$

$cos(F)=\frac{AdjacentSide}{Hypotenuse}=\frac{48}{73}=0.66\\\\tan(F)=\frac{OppositeSide}{AdjacentSide}=\frac{55}{48}=1.15$

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:

$OppositeSide=\sqrt{c^{2}-a^{2}}=\sqrt{73^{2}-48^{2}}=\sqrt{5329-2304} \\OppositeSide=\sqrt{3025}=55$

Then:

$sin(F)=\frac{OppositeSide}{Hypotenuse}=\frac{55}{73}=0.75$

$cos(F)=\frac{AdjacentSide}{Hypotenuse}=\frac{48}{73}=0.66\\\\tan(F)=\frac{OppositeSide}{AdjacentSide}=\frac{55}{48}=1.15$

Have a nice day!

Answer 2

Answer:

Sin F  = 0.7534

Cos F = 0.6575

Tan F= 1.145

Step-by-step 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