Question

I don’t know if I set it up right can I get some help Plss

Answer 1

Given a right angle triangle

The side opposite the given angle is the opposite

The side opposite the right angle is the hypotenuse (the slant side)

The side next to the given angle is the adjacent, as shown below

Given the following dimensions below

`\begin{gathered} Hypotenuse=Hyp=44\text{ units} \\ Opposite=Opp=z\text{ units} \\ \theta=66.7\degree \end{gathered}`

To find the value of z, we apply SOHCAHTOA

Since the hypotenuse and opposite side lengths are given, we apply sine formula which is

`\sin\theta=(Opp)/(Hyp)`

Substitute the values into the formula above

`\sin66.7\degree=(z)/(44)`

Solve for z

`\begin{gathered} \sin66.7\degree=(z)/(44) \\ Crossmultiply \\ z=44*\sin66.7\degree \\ z=40.41164\text{ units} \\ z=40.41\text{ units \lparen nearest hundredth\rparen} \end{gathered}`

Hence, the value of z is 40.41 units (nearest hundredth)