Mathematics, 31.03.2020 03:25, Trackg8101

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

Answers: 2

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answered: magicgeek4980

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

values of the sides can therefore be easily found.

1) b = 2·√2, a = 42) x = y = 2·√2 $3) \ \underline{y = \dfrac{3 \cdot \sqrt{2} }{2}}$ , x = 34) y = 3·√2, x = 6

Reasons:

According to Pythagoras theorem, the relationship between the three

sides of a right triangle are;

$c = \sqrt{a^2 + b^2}$

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.

$tan\theta =\mathrm{\dfrac{Opposite \ side \ to\ angle}{Adjacent\ side \ to\ angle}}$

tan(45°) = 1

Therefore;

Opposite leg = Adjacent leg

a = b

1) The hypotenuse = a

Therefore;

$tan(45^{\circ}) =\dfrac{2 \cdot \sqrt{2} }{b}$

, therefore;

$tan(45^{\circ}) =\dfrac{2 \cdot \sqrt{2} }{b} = 1$

b × 1 = 2·√2

b = 2·√2

The hypotenuse side, a = $\sqrt{{(2 \cdot \sqrt{2})^2 + (2 \cdot \sqrt{2})^2}} = 4$

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

$x = \dfrac{4}{\sqrt{2} } = 2 \cdot \sqrt{2}$

x = y = 2·√2

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

Therefore;

$\dfrac{3 \cdot \sqrt{2} }{2} = y$

$x = \sqrt{\left(\dfrac{3 \cdot \sqrt{2} }{2} \right)^2 +\left(\dfrac{3 \cdot \sqrt{2} }{2} \right)^2 } = \sqrt{\left(\dfrac{9 }{2} \right) +\left(\dfrac{9 }{2} \right) } = \sqrt{9} =3$

x = 3

4) y = 3·√2

Therefore;

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

x = 6

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

answered: alexsysantiago54

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.

answered: Guest

maybe - definition of supplementary angles. im not sure. sorry

step-by-step explanation:

answered: Guest

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.