Question

Write your answers in simplified, rationalized form. DO NOT ROUND

Answer 1

We can use the cosine trigonometric reason to find the hypothenuse WX:

`\begin{gathered} \cos 45=(4)/(WX) \\ WX=(4)/(\cos45)=\frac{4}{\frac{\sqrt[]{2}}{2}}=\frac{8}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{8\sqrt[]{2}}{2}=4\sqrt[]{2} \end{gathered}`

We can use the tangent function to find the leg XY.

`\begin{gathered} \tan 45=(XY)/(4) \\ XY=\tan 45\cdot4 \\ XY=1\cdot4 \\ XY=4 \end{gathered}`

At last, we use the interior angles theorem to find angle X, which states that the sum of all three interior angles of a triangle must sum 180°.

`\begin{gathered} m\angle X+45+90=180 \\ m\angle X=180-90-45 \\ m\angle X=45 \end{gathered}`