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

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

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step-by-step explanation: