A regular pentagon is inscribed in ur let of radius 8cm. find the length of one side of the polygon

9514 1404 393

  9.404 cm

Step-by-step explanation:

A regular polygon with n sides inscribed in a circle of radius r will have a side length given by ...

  s = 2r·sin(180°/n)

For r = 8 and n = 5, this gives a side length of ...

  s = 2·8·sin(180°/5) = 16·sin(36°) ≈ 9.404 . . . cm

Answers:

sin(x) = 3/5

cos(y) = 3/5

They are both equal to the same value

Explanation:

Use the Pythagorean theorem to find the hypotenuse

a^2+b^2 = c^2

8^2+6^2 = c^2

100 = c^2

c^2 = 100

c = sqrt(100)

c = 10

The hypotenuse is 10 units long.

Now compute the sine of angle x.

sin(angle) = oppposite/hypotenuse

sin(x) = 6/10

sin(x) = 3/5

Also, find the cosine of angle y

cos(angle) = adjacent/hypotenuse

cos(y) = 6/10

cos(y) = 3/5

It turns out that sin(x) = cos(y) if and only if x+y = 90.