Question

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.

Answer 1

Side AB = 5√2 or AB =7.1

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

Answer 2

Answer:
`r=5√(2)`≈
`7.07`

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√(2)`≈7.07