Question

Find the values of each variable using sin, cos or sine

Answer 1

To obtain the value of x, substitute the values of the following.

`\begin{gathered} \theta=70\degree \\ \text{opposite side}=x \\ \text{hypothenuse}=30 \end{gathered}`

Thus, we obtain the following

`\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{hypothenuse} \\ \sin 70\degree=(x)/(30) \end{gathered}`

Multiply both sides of the equation by 30 and then simplify.

`\begin{gathered} 30\sin 70\degree=x \\ x\approx28.19 \\ x\approx28 \end{gathered}`

Since the two sides are equal, the base angles must be equal. Thus, we obtain the following.

`\begin{gathered} \theta=70\degree \\ \text{adjacent side}=y \\ \text{hypothenuse}=30 \end{gathered}`

Substitute the values using the following equation.

`\begin{gathered} \cos \theta=\frac{adjacent\text{ side}}{hypothenuse} \\ \cos 70\degree=(y)/(30) \end{gathered}`

Multiply both sides of the equation by 30 and then simplify.

`\begin{gathered} 30\cos 70\degree=y \\ y\approx10.26 \\ y\approx10 \end{gathered}`

Therefore, the value of x is approximately 28.19 and the value of y is approximately 10.26.