Question

What is the value of r?

Answer 1

Answer: $r=5\sqrt{2}$≈$7.07$

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:

$sin\alpha=opposite /hypotenuse$

Where:

$\alpha=45\°\\opposite=5\\hypotenuse=r$

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

$sin(45\°)=5/r\\r=5/sin(45\°)$

$r=5\sqrt{2}$≈7.07

Answer 2

Answer:

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