Answer:
m∠AMO ≈ 54.7°
AΔANM = 486√3
Step-by-step explanation:
The edges are congruent, so all four faces are congruent equilateral triangles. We'll say the length of each edge is 2r.
The height of the pyramid h is given to be 36.
The perpendicular distance from O to line MP is called the apothem (a). Using 30-60-90 triangles, b = 2a and r = a√3.
Use cosine to find m∠AMO.
cos(∠AMO) = b / (2r)
cos(∠AMO) = (2a) / (2a√3)
cos(∠AMO) = 1 / √3
m∠AMO ≈ 54.7°
Use Pythagorean theorem to find the apothem.
(2r)² = b² + h²
(2a√3)² = (2a)² + 36²
12a² = 4a² + 1296
8a² = 1296
a² = 162
a = 9√2
So the edge length is:
2r = 2√3 (9√2)
2r = 18√6
The area of the equilateral triangle ΔANM is half the apothem times the perimeter:
A = ½aP
A = ½ (9√2) (3 × 18√6)
A = 243√12
A = 486√3
Knowing that the tiles are regular polygons, we can deduce that each angle of the tile B is 60. Drawing a circle where a vertex of tile B is the center, we can also deduce that the major angle created by the sides of tile B is 300 because all central angles in a circle add up to 360. Since all A tiles are congruent (they are regular and share the same side), we know that their interior angles are also congruent. Since we know their interior angles add up to 300 (because 2 of their interior angles + 60 = 360), we can divide 300 by 2 to calculate each interior angle, which is 150. By subtracting 150 from 180, we get 30 which is the measure of each EXTERIOR angle of tile A. From basic geometry knowledge, we know that the sum of all exterior angles is 360. Using this, we can divide 360 by 30 to get 10 which is the number of sides of tile A.
Final Answer: Tile A has 10 sides, or in other words is decagon.
Answer:
try A,C and E because A) has more students than any other ones C) if I goes up in twos and E) same as C
Answer:
1 solution
Step-by-step explanation:
If you were to graph this line it would be a straight line so there is 1 solution.
y=3x
x=y/3
