Question

Question: Find the exact values of x and y using appropriate Special Right Triangle theorems. Write your answers in simplest radical form (no rounding).

Answer 1

Since we're on a right triangle, we'll have that:

`\cos (45)=(5)/(x)`

Solving for x,

`\begin{gathered} \cos (45)=(5)/(x) \\ \\ \rightarrow x=(5)/(\cos(45)) \\ \\ \Rightarrow x=5\text{ }\sqrt[]{2} \end{gathered}`

Now, using the pythagorean theroem, we can say that:

`5^2+y^2=x^2`

Solving for y,

`\begin{gathered} 5^2+y^2=x^2 \\ \rightarrow y^2=x^2-5^2 \\ \rightarrow y=\sqrt[]{x^2-5^2} \\ \rightarrow y=\sqrt[]{(5\text{ }\sqrt[]{2})^2-5^2} \\ \rightarrow y=\sqrt[]{50-25} \\ \rightarrow y=\sqrt[]{25} \\ \\ \Rightarrow y=5 \end{gathered}`

Therefore, we can conclude that:

`\begin{gathered} x=5\text{ }\sqrt[]{2} \\ y=5 \end{gathered}`