Answer:
x = 8.69
Step-by-step explanation:
we know that the perimeter of the dodecagon is 54, so each edge will be 54/12
54/12 = 4.5 cm
if we draw the lines to remove 6 vertices and form a hexagon, 6 triangles with 2 sides of 4.5 cm are formed.
we know that the angle of each vertex is 150 ° because it is a dodecagon
if we apply the law of cosines we can take the other side of the triangle, since we only need 2 side and the opposite angle to the side we want to know
a would be our x
b = 4.5
c = 4.5
A = 150°
a^2 = b^2 + c^2 - 2bc * cos (A)
x^2 = 4.5^2 + 4.5^2 - 2 * 4.5 * 4.5 * cos (150)
x^2 = 20.25 + 20.25 - 40.50 * -0.866
x^2 = 40.50 + 35.07
x = √ 75.57
x = 8.69
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Answer: 7
Step-by-step explanation:
denotes the intersection of A and C, or in other words, how many elements are shared between them.
The number of elements is 2 + 5 = 7
Answer:3.73248×10^5
Step-by-step explanation:
To write (12*6)^3 as a single power,
We gets
12 × 6=72
Therefore 72^2
=373248
As a single power
3.73248×10^5
Answer:
√7 ≈ 2.646
Step-by-step explanation:
The law of cosines is applicable. It tells you ...
c² = a² + b² - 2ab·cos(C) . . . . . where a, b, c are triangle side lengths, and angle C is opposite side c.
Filling in the given information, you have ...
c² = 2² + 3² - 2·2·3·cos(60°) = 4 + 9 - 12·(1/2) = 7
c = √7 ≈ 2.646
The length of the third side is √7, about 2.646 units.
