Can anyone help with any of these?
1 answer:
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Answer:
One scientist was working two molecules:
And verified that geometrically speaking, those are trigonal planar molecules made up of an equilateral triangle. He designed both molecules and classified them as Plane dihedral Groups. Was he correct? Why?
Step-by-step explanation:
Yes He was right. Place one atom in the centroid of the equilateral triangle (S or B), and each atom in each vertex(O or F).
We can apply geometric transformations (plane) rotations: R0, R2π/3, R4π/3
(And spatial ones, as R1, R2, R3 180º rotation over each median.)
Composite functions show that this is not an Abelian Group:
Draw ΔABC as shown in the figure below.
m∠B = 137°, b = 14, c = 9.
From the Law of Sines,
sin(C)/c = sin(B)/b
or
sin(C)/9 = sin(137°)/14
sin(C) = (9/14)*sin(137°) = 0.4384
m∠C = arcsin(0.4384) = 26°
Because the sum of angles in a triangle is 180°, therefore
m∠A = 180 -137 - 26 = 17°
From the Law of Sines,
a/sin(A) = b/sin(B)
or
a/sin(17°) = 14/sin(137°)
a = (sin(17°)/sin(127°))*14 = 6
Answer:
The solution for the triangle is
a = 6, b = 14, c = 9
m∠A = 17°, m∠B = 137°, m∠C = 26°
m∠B = 137°, b = 14, c = 9.
From the Law of Sines,
sin(C)/c = sin(B)/b
or
sin(C)/9 = sin(137°)/14
sin(C) = (9/14)*sin(137°) = 0.4384
m∠C = arcsin(0.4384) = 26°
Because the sum of angles in a triangle is 180°, therefore
m∠A = 180 -137 - 26 = 17°
From the Law of Sines,
a/sin(A) = b/sin(B)
or
a/sin(17°) = 14/sin(137°)
a = (sin(17°)/sin(127°))*14 = 6
Answer:
The solution for the triangle is
a = 6, b = 14, c = 9
m∠A = 17°, m∠B = 137°, m∠C = 26°