Um I'm good that looks so confusing sorry. TwT
Answer:
![a=10.92 units](https://tex.z-dn.net/?f=a%3D10.92%20units)
![b=14.51 units](https://tex.z-dn.net/?f=b%3D14.51%20units)
Step-by-step explanation:
We are given that c=6 units
![\angle A=43^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20A%3D43%5E%7B%5Ccirc%7D)
![\angle B=115^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20B%3D115%5E%7B%5Ccirc%7D)
We have to find the side length a and b.
We know that sum of angles of a triangle =180 degrees
![\angle A+\angle B+\angle C=180](https://tex.z-dn.net/?f=%5Cangle%20A%2B%5Cangle%20B%2B%5Cangle%20C%3D180)
Substitute the values then we get
![43+115+\angle C=180](https://tex.z-dn.net/?f=43%2B115%2B%5Cangle%20C%3D180)
![158+\angle C=180](https://tex.z-dn.net/?f=158%2B%5Cangle%20C%3D180)
![\angle C=180-158=22^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20C%3D180-158%3D22%5E%7B%5Ccirc%7D)
sine law: ![\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%20A%7D%3D%5Cfrac%7Bb%7D%7Bsin%20B%7D%3D%5Cfrac%7Bc%7D%7Bsin%20C%7D)
![\frac{a}{sin 43^{\circ}}=\frac{6}{sin 22^{\circ}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%2043%5E%7B%5Ccirc%7D%7D%3D%5Cfrac%7B6%7D%7Bsin%2022%5E%7B%5Ccirc%7D%7D)
![a=\frac{6}{sin 22^{\circ}}\times sin 43^{\circ}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B6%7D%7Bsin%2022%5E%7B%5Ccirc%7D%7D%5Ctimes%20sin%2043%5E%7B%5Ccirc%7D)
![a=10.92 units](https://tex.z-dn.net/?f=a%3D10.92%20units)
![\frac{b}{sin 115^{\circ}}=\frac{6}{sin 22^{\circ}}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Bsin%20115%5E%7B%5Ccirc%7D%7D%3D%5Cfrac%7B6%7D%7Bsin%2022%5E%7B%5Ccirc%7D%7D)
![b=\frac{6}{sin 22^{\circ}}\times sin 115^{\circ}=14.51](https://tex.z-dn.net/?f=%20b%3D%5Cfrac%7B6%7D%7Bsin%2022%5E%7B%5Ccirc%7D%7D%5Ctimes%20sin%20115%5E%7B%5Ccirc%7D%3D14.51)
![b=14.51 units](https://tex.z-dn.net/?f=b%3D14.51%20units)
The volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)
<h3>How to determine the volume?</h3>
The complete question is added as an attachment
From the attached image, we have:
Length = 12 - 2x
Width = 7 - 2x
Height = x
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
Volume = (12 - 2x) * (7 - 2x) * x
This gives
Volume = x(12 - 2x)(7 - 2x)
Hence, the volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)
Read more about polynomial at:
brainly.com/question/4142886
#SPJ1
Answer:
25π units^2
Step-by-step explanation:
The shape is a quarter circle with radius 10 units.
area of circle = πr^2
area of a quarter circle = (1/4)π(10 units)^2
area = 25π units^2