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dem82 [27]
2 years ago
12

I need serious help with this! I'll give 20 points!

Mathematics
1 answer:
GrogVix [38]2 years ago
7 0

Answer:

glizzy

Step-by-step explanation:

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A regular octagon is inscribed in a circle with a radius of 10 cm. What is the length of one side of the octagon?
Semenov [28]

Answer:

The length of one side of the octagon is 7.65 cm

Step-by-step explanation:

The parameters given are;

A regular octagon inscribed in a circle of radius, r, of 10 cm.

The length of each side is found from the isosceles triangle formed by the radius and one side of the octagon

The sum of interior angles in a polygon, ∑θ_i = 180 × (n - 2)

Where;

n = The number of sides of the polygon

θ_i = The interior angle of the polygon

For the octagon, we have;

n = 8, therefore;

∑θ_i = 180 × (8 - 2) = 1080

Given that there are eight equal angles in a regular octagon, we have;

∑θ_i = 8 × θ_i = 1080

θ_i = 1080/8 = 135°

The sum of angles at the center of the circle = 360

Therefore, the angle at the center (tip angle) of the isosceles triangle formed by the radius and one side of the octagon = 360/8 = 45°

The base angles of the isosceles triangle is therefore, (180 - 45)/2 = 67.5° = θ_i/2

The length of the base of the isosceles triangle formed by the radius and one side of the octagon = The length of one side of the octagon

From trigonometric ratios, the length of the base of the isosceles triangle is therefore;

2 × r × cos(θ_i/2) = 2×10 × cos(67.5°) = 7.65 cm

The length of the base of the isosceles triangle = 7.65 cm = The length of one side of the octagon.

7 0
3 years ago
Read 2 more answers
I need help answering
Arte-miy333 [17]
1/2(7)(4)

= 14 cm

Hope this help
7 0
3 years ago
Read 2 more answers
Which system of equations has no solutions?
baherus [9]

Answer:

A

Step-by-step explanation:the lines do not cross therefor the two equations do not share a solution.

5 0
3 years ago
Please help ? Thanks
rjkz [21]
Try answer C or B because either one could be the right answer
8 0
3 years ago
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A number to the 12th power divided by the same number to the 9th power equals 64 what is the number
Bess [88]

Answer:

The statement written as a formula is. a12a9=125. We can simplify the fraction, and we have. a3=125. To solve for a , take the third root

Step-by-step explanation:

8 0
3 years ago
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