Answer:
Step-by-step explanation:
Suppose we have a general triangle like the one shown in the figure.
We know the angle A, the angle B and the length b.
![A = 30\°\\\\B = 45\°\\\\b = 10](https://tex.z-dn.net/?f=A%20%3D%2030%5C%C2%B0%5C%5C%5C%5CB%20%3D%2045%5C%C2%B0%5C%5C%5C%5Cb%20%3D%2010)
By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.
So
![A + B + C = 180\\\\30 + 45 + C = 180](https://tex.z-dn.net/?f=A%20%2B%20B%20%2B%20C%20%3D%20180%5C%5C%5C%5C30%20%2B%2045%20%2B%20C%20%3D%20180)
We solve the equation and thus we find the angle C.
![C = 180 - 30-45\\\\C = 105](https://tex.z-dn.net/?f=C%20%3D%20180%20-%2030-45%5C%5C%5C%5CC%20%3D%20105)
We already know the three triangle angles.
Now we use the sine theorem to calculate the sides c and a.
The sine theorem says that:
![\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28A%29%7D%7Ba%7D%3D%5Cfrac%7Bsin%28B%29%7D%7Bb%7D%3D%5Cfrac%7Bsin%28C%29%7D%7Bc%7D)
Then
![\frac{sin(30)}{a}=\frac{sin(45)}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%2830%29%7D%7Ba%7D%3D%5Cfrac%7Bsin%2845%29%7D%7B10%7D)
![\frac{sin(30)}{\frac{sin(45)}{10}}=a](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%2830%29%7D%7B%5Cfrac%7Bsin%2845%29%7D%7B10%7D%7D%3Da)
![a=7.071](https://tex.z-dn.net/?f=a%3D7.071)
Also
![\frac{sin(105)}{c}=\frac{sin(45)}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28105%29%7D%7Bc%7D%3D%5Cfrac%7Bsin%2845%29%7D%7B10%7D)
![\frac{sin(105)}{\frac{sin(45)}{10}}=c](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28105%29%7D%7B%5Cfrac%7Bsin%2845%29%7D%7B10%7D%7D%3Dc)
![c=13.660](https://tex.z-dn.net/?f=c%3D13.660)
Finally, we use the Heron formula to calculate the triangle area
![A=\sqrt{s(s-a)(s-b)(s-c)}](https://tex.z-dn.net/?f=A%3D%5Csqrt%7Bs%28s-a%29%28s-b%29%28s-c%29%7D)
Where s is:
![s=\frac{a+b+c}{2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D)
Therefore
![s=\frac{7.071+10+13.660}{2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B7.071%2B10%2B13.660%7D%7B2%7D)
![s=15.37](https://tex.z-dn.net/?f=s%3D15.37)
![A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}](https://tex.z-dn.net/?f=A%3D%5Csqrt%7B15.37%2815.37-7.071%29%2815.37-10%29%2815.37-13.66%29%7D)
Answer: B
Step-by-step explanation:
A factorial is multiplying the integer and all of the integers below it together.
15 I may be wrong but If I am please provide more information.
Calculate for the mean/ average of the given numbers:
μ = (1 + 2 + 3 + 4 + 5) / 5 = 3
Then, we calculate for the summation of the squares of differences of these numbers from the mean, S
S = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²
S = 10
Divide this summation by the number of items and take the square root of the result to get the standard deviation.
SD = sqrt (10 / 5) = sqrt 2
SD = 1.41
Thus, the standard deviation of the given is equal to 1.41.