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3 years ago

Find the exact length of the third side.

Mathematics

2 answers:

KATRIN_1 [288]3 years ago

7 0

Answer:

The third side is sqrt(5)

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

We know the legs are 1 and 2 and we are looking for the hypotenuse.

1^2+2^2 = c^2

1+4 = c^2

5 =c^2

Take the square root of each side

sqrt(5) = sqrt(c^2)

sqrt(5) =c

The third side is sqrt(5)

adell [148]3 years ago

6 0

Answer:

$\sqrt{5}$ or 2.236

Step-by-step explanation:

The pythagorem theorm states that side 1^2 + side^2 = hypotenuse^2

2^2 + 1^2 = h^2

4+1 = h^2

5 = h^2

$\sqrt{5} = \sqrt{h^{2} }$

$\sqrt{5} =h$

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3 years ago

Step 1: Choose ONE of the following triangles and complete the table below:

Archy [21]

The question is incomplete below you will find the missing part.

Step 1 : Choose ONE of the following triangles complete the table below:

1. Obtuse Scalene Triangle Translation to prove SSS Congruence

2. Isosceles Right Triangle Reflection to prove ASA Congruence

3. Equilateral Equiangular Triangle Rotation to prove SAS Congruence

Original Coordinate Point

Transformation Rule

Image Coordinate Points

A (1, 4) (x,y) -> (x+ ,y -) A’ ( , )

B ( 7,4) (x,y) -> (x+ ,y - ) B’ ( , )

C (8,9) (x,y) -> (x+ ,y -) C’ ( , )

The appropriate table is also shown below.

The triangles ABC and A'B'C' are congruent by SSS through Obtuse Scalene Triangle Translation because the corresponding sides are congruent

Two triangles are congruent if their size and shape are the same.

Now we have to transform the triangle,

The coordinates of the triangle ΔABC are given as:

A = (1, 4)

B = (7,4)

C = (8,9)

so the lengths of the sides of the triangle are given by

AB= √(7-1)²+(4-4)²= √6²= 6

BC= √(8-7)²+(9-4)²= √1²+5²= √1+25= √26

CA= √(8-1)²+(9-4)²= √7²+5²= √49+25= √74

In order to prove the SSS congruence, we have to transform the triangles under the following translation rule:

(x,y) -> (x -3, y +6)

in the above translation,

The triangle will be translated 3 units left

And then translated 6 units up.

So, we have the new coordination of the points of the translated triangle ΔA'B'C'

A' = (1-3, 4+6)

A' = (-2, 10)

B' = (7-3, 4+6)

B' = (4, 10)

C' = (8-3, 9+6)

C' = (5, 15)

Now

so the lengths of the sides of the triangle are given by

A'B'= √(4-(-2))²+(10-10)²= √6²= 6

B'C'= √(5-4)²+(15-10)²= √1²+5²= √1+25= √26

C'A'= √(-2-5)²+(10-15)²= √(-7)²+(-5)²= √49+25= √74

By comparing two triangles ΔABC and ΔA'B'C'

AB ≅ A'B'

BC ≅ B'C'

CA ≅ C'A'

Hence ΔABC ≅ A'B'C' (By S-S-S rule)

By the above transformation, the triangles ABC and A'B'C' are congruent by SSS because the corresponding sides are congruent as all the points are gone through the same transformation.

Learn more about the transformation

here: brainly.com/question/4289712

#SPJ10