What is the value of r?

triangle a b c has right angle c with hypotenuse labeled r. angle a is 45 degrees and its opposite side b c is labeled 5.

enter your answer, as an exact value, in the box.

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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:

Where:

2. When you substitute the values above and solve for the hypotenuse, you obtain:

≈7.07

Side AB = 5√2 or AB =7.1

Step-by-step explanation:

In the diagram attached we can see that Hypotenuse AB has been labeled as

r, angle A is 45° and opposite side BC is 5.

As we know in any right angle triangle sine of an angle = Height/Hypotenuse

Therefore sin45°=5/r

r = 5/sin45° = 5÷1/√2 = 5√2

Therefore side AB = 5√2 = 7.1