A regular hexagon is shown.
2 answers:
Answer:
(C)9 in.
Step-by-step explanation:
The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.
Given the hexagon with a radius of 10 inches
The apothem AB divides the side of the hexagon into two equal parts of 5 Inches as seen in the attached diagram.
Using Pythagoras Theorem
<u>The correct option is C</u>
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Given only one side and two angles, the law of sines is the appropriate choice. To use that, you need to know the angles opposite the side of interest and the given side.
∠C = 180° - ∠A - ∠B
∠C = 180° - 35° - 65° = 80°
Now, the law of sines tells you
b/sin(B) = c/sin(C)
b = c·sin(B)/sin(C) . . . . . multiply by sin(B)
b = 15·sin(65°)/sin(80°)
b ≈ 13.8
_____
Or you can use a triangle solver.
∠C = 180° - ∠A - ∠B
∠C = 180° - 35° - 65° = 80°
Now, the law of sines tells you
b/sin(B) = c/sin(C)
b = c·sin(B)/sin(C) . . . . . multiply by sin(B)
b = 15·sin(65°)/sin(80°)
b ≈ 13.8
_____
Or you can use a triangle solver.