Question

Hey can anyone help me I am really stuck, Use exact values. NO DECIMALS they say

Answer 1

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) =
`(Opposite.Side)/(Hypotenuse)`

cos(θ) =
`(Adjacent.Side)/(Hypotenuse)`

tan(θ) =
`(Opposite.Side)/(Adjacent.Side)`

For this problem, we will only be using the trigonometric functions of Sine and Tangent.

Start by finding x.

sin(30) =
`(4)/(x)`

Multiply x to both sides.

x × sin(30) =
`(4)/(x)` × x

x(sin(30)) = 4

Divide both sides of the equation by sin(30).

x(sin(30)) ÷ (sin(30)) = 4 ÷ (sin(30))

x =
`(4)/(sin(30))`

Simplify in calculator.

x = 8

Now find the value of y.

tan(30) =
`(4)/(y)`

Multiply y to both sides.

y × tan(30) =
`(4)/(y)` × y

y(tan(30)) = 4

Divide both sides of the equation by tan(30).

y(tan(30)) ÷ (tan(30)) = 4 ÷ (tan(30))

y =
`(4)/(tan(30))`

Simplify in calculator.

y =
`4√(3)`

x = 8

y =
`4√(3)`

^ These are the answers.

I hope this helps!

#teamtrees #PAW (Plant And Water)

Answer 2

x = 8

y = 4 sqrt(3)

Explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 30 = 4/x

x sin 30 = 4

x = 4 / sin 30

x = 4 / ( 1/2)

x = 8

tan theta = opp /adj

tan 30 = 4/y

y tan 30 =4

y = 4 / tan 30

y = 4 / ( 1/ sqrt(3))

y = 4 sqrt(3)