Answer:
Step-by-step explanation:
The supplement of 102 = 180 - 102 = 78
It is the interior angle of the given exterior angle.
It is also the enclosed angle of the isosceles triangle
Each of the other two angles = y
180 = 2*y + 78 Subtract 78 from both sides
180 - 78 = 2y Combine
102 = 2y Divide by 2
102 / 2 = y
51 = y
The smaller triangle on your right has 2 equal sides that are marked.
The angle you just found = <2 and the vertically opposite angle of the 51
So <2 = 51
Answer:
60°
Step-by-step explanation:
We'll begin by calculating EC. This can be obtained as follow:
Angle EAC = 39°
Hypothenus = EA = 3.7 m
Opposite = EC =?
Sine EAC = Opposite /Hypothenus
Sine 39 = EC / 3.7
Cross multiply
EC = 3.7 × Sine 39
EC = 2.3 m
Finally, we shall determine angle BEC. This can be obtained as follow:
Adjacent = EC = 2.3 m
Hypothenus = BC = 4.6 m
Angle BEC =?
Cos BEC = Adjacent / Hypothenus
Cos BEC = 2.3 / 4.6
Cos BEC = 0.5
Take the inverse of Cos
BEC = Cos¯¹ 0.5
BEC = 60°
Thus, angle BEC is 60°
In this item, we are informed that the order of the entries does not matter in determination the number of ways in which the Archie can choose for his party. Because the arrangement or order is not important, this type of problem uses the concept of COMBINATION.
The equation for combination is,
nCr = n!/((n - r)!(r!))
nCr is read as "combination of n taken r".
Substituting the known values to the equation,
15C6 = 15! / ((15 - 6)!(6!))
= 5005
Hence, there are 5005 ways in which Archee can choose the 6 entrees for his party.
