Find the missing side lengths. Leave your answers as radicals in the simplest form.

The special right triangles have the property of equal leg lengths and the

values of the sides can therefore be easily found.

Reasons:

According to Pythagoras theorem, the relationship between the three

sides of a right triangle are;

Where;

c = The length of the hypotenuse side

a and b = The legs of the triangle

The right triangles are special triangles having 45° as one of the angles.

tan(45°) = 1

Therefore;

Opposite leg = Adjacent leg

a = b

1) The hypotenuse = a

Therefore;

, therefore;

b × 1 = 2·√2

b = 2·√2

The hypotenuse side, a =

a = 4

2) Given that one of the angles of the right triangle is 45°, we have that the

leg lengths are equal, therefore;

y = x,

The length of the hypotenuse side, c = 4

Which gives;

4 = √(x² + y²) = √(x² + x²) = √(2·x²) = (√2)·x

x = y = 2·√2

3) One of the angles of the right triangle is 45°

Therefore;

x = 3

4) y = 3·√2

Therefore;

x = √((3·√2)² + (3·√2)²) = √(18 + 18) = 6

x = 6

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1. a =4; b = 2√2

2. x= 2√2; y= 2√2

3. x = 3; y = 3√2/2

4. x = 6; y = 3 √ 2

Step-by-step explanation:

Let's attempt solving this!

KEYNOTE:

1. In a 45° / 90° triangle, the legs are congruent

2. In a 45° / 90° triangle, the hypotenuse = √2

3. Both legs are of thesame length.

4. Hypotenuse is always one of the exact length Multiplied by the square root of 2.

Please find the attached file.