Answer: [tex]r=5\sqrt{2}[/tex]≈[tex]7.07[/tex]
Step-by-step explanation:
1. You know that the triangle described in the problem is a right triangle and the problem gives the length of the opposite side. Therefore, you can calculate the lenght of the hypotenuse as following:
[tex]sin\alpha=opposite /hypotenuse[/tex]
Where:
[tex]\alpha=45\°\\opposite=5\\hypotenuse=r[/tex]
2. When you substitute the values above and solve for the hypotenuse, you obtain:
[tex]sin(45\°)=5/r\\r=5/sin(45\°)[/tex]
[tex]r=5\sqrt{2}[/tex]≈7.07
