Question 1:
By definition, the area of a regular hexagon, depending on its sides, is given by:
[tex]A = \frac{3 \sqrt{3}L^2}{2}
[/tex]
Where,
L: side of the regular hexagon.
Substituting values we have:
[tex]A = \frac{3 \sqrt{3}12^2}{2} [/tex]
[tex]A = 374.1229744
[/tex]
Rounding to the nearest hundredth we have:
[tex]A = 374.12 cm ^ 2
[/tex] Answer:
The area of a regular hexagon with a side length of 12 cm is:
[tex]A = 374.12 cm ^ 2 [/tex]
Question 2:
By definition, sides of a triangle 30-60-90 are given by:
Largest side:[tex] \sqrt{3}x[/tex]
Smallest side: x
hypotenuse: 2x
Therefore, since the smallest side length measures 5 cm, then the hypotenuse is:
[tex]2x = 2 * 5 = 10 cm
[/tex]
Answer:
the length of the hypotenuse when the shorter leg is 5 cm is:
10 cm
Question 3:
The first thing you should know for this case, is that angle 30, is a notable angle.
Therefore, the values of the sine are defined for notables angles.
The notable angles are:
0, 30, 45, 60, 90
Therefore, the value of sine (30) is given by:
sine (30) = 1/2
Answer:
the exact value of sin 30 ° is:
sine (30) = 1/2
