The special right triangles have the property of equal leg lengths and the
values of the sides can therefore be easily found.
- [tex]3) \ \underline{y = \dfrac{3 \cdot \sqrt{2} }{2}}[/tex], x = 3
Reasons:
According to Pythagoras theorem, the relationship between the three
sides of a right triangle are;
[tex]c = \sqrt{a^2 + b^2}[/tex]
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.
[tex]tan\theta =\mathrm{\dfrac{Opposite \ side \ to\ angle}{Adjacent\ side \ to\ angle}}[/tex]
tan(45°) = 1
Therefore;
Opposite leg = Adjacent leg
a = b
1) The hypotenuse = a
Therefore;
[tex]tan(45^{\circ}) =\dfrac{2 \cdot \sqrt{2} }{b}[/tex]
, therefore;
[tex]tan(45^{\circ}) =\dfrac{2 \cdot \sqrt{2} }{b} = 1[/tex]
b × 1 = 2·√2
b = 2·√2
The hypotenuse side, a = [tex]\sqrt{{(2 \cdot \sqrt{2})^2 + (2 \cdot \sqrt{2})^2}} = 4[/tex]
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
[tex]x = \dfrac{4}{\sqrt{2} } = 2 \cdot \sqrt{2}[/tex]
x = y = 2·√2
3) One of the angles of the right triangle is 45°
Therefore;
[tex]\dfrac{3 \cdot \sqrt{2} }{2} = y[/tex]
[tex]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[/tex]
x = 3
4) y = 3·√2
Therefore;
x = √((3·√2)² + (3·√2)²) = √(18 + 18) = 6
x = 6
Learn more here:
https://brainly.com/question/3235351
