Explanation
First triangle
Since it is a right triangle, we can use the trigonometric ratio tan(θ) to find the length b.
[tex]\tan(\theta)=\frac{\text{ Opposite side}}{\text{ Adjacent side}}[/tex]
So, we have:
[tex]\begin{gathered} \tan(\theta)=\frac{\text{ Opposite side}}{\text{ Adjacent side}} \\ \tan(60°)=\frac{b}{7} \\ \text{ Multiply by 7 from both sides} \\ \tan(60)*7=\frac{b}{7}*7 \\ \sqrt{3}*7=b \\ 7\sqrt{3}=b \end{gathered}[/tex]
Second triangle
Since it is a right triangle, we can use the trigonometric ratio cos(θ) to find the length a.
[tex]\cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}}[/tex]
So, we have:
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos(45\degree)=\frac{a}{5} \\ \text{ Multiply by 5 from both sides} \\ \cos(45\degree)*5=\frac{a}{5}*5 \\ \frac{\sqrt{2}}{2}*5=a \\ \frac{5\sqrt{2}}{2}=a \end{gathered}[/tex]Answer[tex]\begin{gathered} b=7\sqrt{3} \\ a=\frac{5\sqrt{2}}{2} \end{gathered}[/tex]
