Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical fo
1 answer:
17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.
<h3>How do you find the length of the diagonal of a regular hexagon?</h3>Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.
For a polygon, the SUM of the internal angles is:
(n-2) * 180 (n=6 for hexagon)
(6-2)*180 = 720 Thus EACH angle is : 720/6 = 120 degrees
Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.
There are 180 degrees in any triangle:
(180-120) / 2 = 30 degrees for each of the smaller angles.
Now use the law of sines:
10/sin30 = x/(sin120)
10/(.5) × (sqrt3 )/ 2 = x
10 sqrt 3
10/sin30 × sin 120 = 17.32
17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.
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Answer:
From least to greatest, the correct order is: ; -7.666....; -7.64; and
.
Step-by-step explanation:
Since is the only positive number, that means that it will be the greatest number on the list.
is equivalent to -7.85, which makes it the smallest number. So you can conclude that the correct order is
; -7.666...; -7.64; and
.