Answer:
2 sqrt(3) = n
k = 4 sqrt(3)
Step-by-step explanation:
We know that cos 30 = adjacent/ hypotenuse
cos 30 = 6 /k
Multiply each side by k
k cos 30 = 6k * k
k cos 30 = 6
Divide each side by cos 30
k cos 30/ cos 30 = 6/ cos 30
k = 6 / cos 30
k = 6/ (sqrt(3)/2)
k =12 / sqrt(3)
We cannot leave the sqrt in the denominator
k = 12 / sqrt(3) * sqrt(3)/sqrt(3)
k = 12 sqrt(3)/3
k = 4 sqrt(3)
We know tan 30 = opposite/adjacent
tan 30 = n/6
Multiply each side by 6
6 tan 30 = n
6 * (sqrt(3)/3) = n
6/3 * sqrt(3) = n
2 sqrt(3) = n
Answer:
7.5
Step-by-step explanation:
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To convert a mixed number into an improper fraction, you can multiply the denominator of the fraction by the whole number. Then, you add the product with the numerator to get the new numerator. The denominator remains the same.
Answer:umm
Step-by-step explanation:
4/3 of the area of the larger hexagon to the area of the smaller hexagon
Let the sides of the interior hexagon be 2 cm long, then this hexagon is made up of 6 equilateral triangles of side = 2.
The area of this hexagon = 6 * 1 * sqrt3 = 6 sqrt3 ( as the triangle is made up of 2 60-30-90 triangles)
The exterior hexagon is made up of 6 equilateral triangles with altitude 2 and the area = 6 * 2 * (2 / sqrt3 ) = 24 / sqrt3
area exterior hex / interior hex = 24 / sqrt3 * 1 / 6sqrt3 = 24/18
= 4/3
Required ratio = 4/3 answer
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