Question

Find the value of the variable in the diagram to the nearest hundredth

Answer 1

Let's begin by listing out the given information:

`\begin{gathered} x(opposite)=\text{?} \\ \theta=25^(\circ) \\ hypotenuse=41 \end{gathered}`

We will calculate for x using the Trigonometric ratio (SOHCAHTOA). In this case, SOH

`\begin{gathered} \text{SOH}\Rightarrow sin\theta=(opposite)/(hypotenuse) \\ sin25^(\circ)=(x)/(41) \\ x=41\cdot sin25^(\circ)=17.327\approx17.33 \\ x=17.33 \end{gathered}`