Answer and Step-by-step explanation:
To solve, we need to use Trigonometric Functions.
These functions include Sine, Cosine, and Tangent.
- Each one has its own rule to follow when solving.
θ = Angle
sin(θ) = [tex]\frac{Opposite.Side}{Hypotenuse}[/tex]
cos(θ) = [tex]\frac{Adjacent.Side}{Hypotenuse}[/tex]
tan(θ) = [tex]\frac{Opposite.Side}{Adjacent.Side}[/tex]
For this problem, we will only be using the trigonometric functions of Sine and Tangent.
Start by finding x.
sin(30) = [tex]\frac{4}{x}[/tex]
Multiply x to both sides.
x × sin(30) = [tex]\frac{4}{x}[/tex] × x
x(sin(30)) = 4
Divide both sides of the equation by sin(30).
x(sin(30)) ÷ (sin(30)) = 4 ÷ (sin(30))
x = [tex]\frac{4}{sin(30)}[/tex]
Simplify in calculator.
x = 8
Now find the value of y.
tan(30) = [tex]\frac{4}{y}[/tex]
Multiply y to both sides.
y × tan(30) = [tex]\frac{4}{y}[/tex] × y
y(tan(30)) = 4
Divide both sides of the equation by tan(30).
y(tan(30)) ÷ (tan(30)) = 4 ÷ (tan(30))
y = [tex]\frac{4}{tan(30)}[/tex]
Simplify in calculator.
y = [tex]4\sqrt{3}[/tex]
x = 8
y = [tex]4\sqrt{3}[/tex]
^ These are the answers.
I hope this helps!
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