Question

Find the value of x and the value of y.A. X= 5, y = 5sqrt2B. X=5sqrt2, y=5C. X=5sqrt2/2, y= 5D.x = 5, y =5sqrt2/2

Answer 1

Concept

To find the values of x and y, you apply the trigonometry ratio formula.

`\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \theta=45^o \end{gathered}`

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.

`\begin{gathered} \text{From} \\ \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \sin 45\text{ = }(5)/(x) \\ \frac{1}{\sqrt[]{2}}\text{ = }(5)/(x) \\ \text{Cross multiply} \\ x\text{ = 5}\sqrt[]{2} \end{gathered}`

Step 3: find the value of y using tangent angle.

`\begin{gathered} \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \tan 45\text{ = }(5)/(y) \\ \text{When you punch your calculator, tan45 = 1} \\ \text{Therefore,} \\ 1\text{ = }(5)/(y) \\ \text{Cross multiply} \\ y\text{ = 5} \end{gathered}`

Final answer

Option B