Question

How do I know where which choices below go into the correct blanks for number 1-4?

Answer 1

For 1, we have the following triangle:

Using the cosine function to get the hypotenuse we get:

`\begin{gathered} \cos (45)=(7)/(h) \\ \Rightarrow h=(7)/(\cos(45))=\frac{7}{\frac{1}{\sqrt[]{2}}}=7\cdot\sqrt[]{2} \\ h=7\cdot\sqrt[]{2} \end{gathered}`

Now that we have the hypotenuse, we can find the remaining side using the pythagorean theorem:

`\begin{gathered} h^2=7^2+x^2 \\ \Rightarrow x^2=h^2-7^2=(7\cdot\sqrt[]{2})^2-7^2=49\cdot2-49=49 \\ \Rightarrow x^2=49 \\ x=7 \end{gathered}`

Therefore, the value of the remaining side is 7.