Concept
To find the values of x and y, you apply the trigonometry ratio formula.
[tex]\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \theta=45^o \end{gathered}[/tex]
Step 1: Name the given sides
Opposite = 5 side facing the given angle 45 degrees
Hypotenuse = x side facing the right angle
Adjacent = y the third side
Step 2: Substitute the values of the sides to find the unknown.
[tex]\begin{gathered} \text{From} \\ \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \sin 45\text{ = }\frac{5}{x} \\ \frac{1}{\sqrt[]{2}}\text{ = }\frac{5}{x} \\ \text{Cross multiply} \\ x\text{ = 5}\sqrt[]{2} \end{gathered}[/tex]
Step 3: find the value of y using tangent angle.
[tex]\begin{gathered} \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \tan 45\text{ = }\frac{5}{y} \\ \text{When you punch your calculator, tan45 = 1} \\ \text{Therefore,} \\ 1\text{ = }\frac{5}{y} \\ \text{Cross multiply} \\ y\text{ = 5} \end{gathered}[/tex]
Final answer
Option B
