9514 1404 393
Answer:
1) 135°
2) 0.77 units
3) 0.92 units
4) 6.12 units
5) 2.83 square units
Step-by-step explanation:
1) The exterior angle at any vertex is 360°/n, where n is the number of sides. For the octagon, the exterior angle is 360°/8 = 45°. The interior angle will be the supplement of this: 180° -45° = 135°.
The measure of each interior angle is 135°.
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2) Each sector of the octagon is an isosceles triangle with a central angle of 45° (also 360°/8). Since the radius is 1 unit, the length of one side is twice the sine of half the central angle.
s = 2·sin(45°/2) ≈ 0.765367
The length of one side is about 0.77 units.
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3) Similarly, the apothem is the cosine of half the central angle:
a = cos(45°/2) ≈ 0.923880
The apothem is about 0.92 units.
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4) For an octagon, the perimeter is 8 times the length of one side.
P = 8s = 8(0.765367) ≈ 6.12293
The perimeter is about 6.12 units.
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5) The area of one sector (isosceles triangle) is given by the formula ...
A = (1/2)bh
A = 1/2sa ≈ 1/2(0.765367)(0.923880) ≈ 0.353553
Then the area of the octagon is 8 times this:
A = 8(sector area) = 8(0.353553) ≈ 2.82843
The octagon area is about 2.83 square units.
Answer:
D. m∠A=43, m∠B=55, a=20
Step-by-step explanation:
Given:
∆ABC,
m<C = 82°
AB = c = 29
AC = b = 24
Required:
m<A, m<C, and a (BC)
SOLUTION:
Find m<B using the law of sines:
m<B = 55°
Find m<A:
m<A = 180 - (82 + 55) => sum of angles in a triangle.
= 180 - 137
m<A = 43°
Find a using the law of sines:
Cross multiply
(approximated)
Answer:
Step-by-step explanation:
1. A number written in scientific notation has the following form:
Where is is a number between 1 and 10 but not including 10, and b is an integer.
2. The negative exponent indicates the number of places the decimal point must be moved to the left to obtain the number as a decimal number.
3. Keeping this on mind, you can know that: if the exponent of a number written in scientific notation indicates that the decimal point must be moved 5 places to the left and another number written in scientific notation indicates that the decimal point must be moved 2 places to the left, then the first number is smaller than the second one.
4. Therefore, you can arrange the numbers given in the problem as following: