Answer:
![a=36.87\ units](https://tex.z-dn.net/?f=a%3D36.87%5C%20units)
![B=57.47^o](https://tex.z-dn.net/?f=B%3D57.47%5Eo)
![C=71.53^o](https://tex.z-dn.net/?f=C%3D71.53%5Eo)
Step-by-step explanation:
step 1
Find the length side a
Applying the law of cosines
![a^2=b^2+c^2-2(b)(c)cos(A)](https://tex.z-dn.net/?f=a%5E2%3Db%5E2%2Bc%5E2-2%28b%29%28c%29cos%28A%29)
substitute the given values
![a^2=40^2+45^2-2(40)(45)cos(51^o)](https://tex.z-dn.net/?f=a%5E2%3D40%5E2%2B45%5E2-2%2840%29%2845%29cos%2851%5Eo%29)
![a^2=1,359.4466](https://tex.z-dn.net/?f=a%5E2%3D1%2C359.4466)
![a=36.87\ units](https://tex.z-dn.net/?f=a%3D36.87%5C%20units)
step 2
Find the measure of angle B
Applying the law of sines
![\frac{a}{sin(A)} =\frac{b}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%5Cfrac%7Bb%7D%7Bsin%28B%29%7D)
substitute the given values
![\frac{36.87}{sin(51^o)} =\frac{40}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7B36.87%7D%7Bsin%2851%5Eo%29%7D%20%3D%5Cfrac%7B40%7D%7Bsin%28B%29%7D)
![sin(B)=\frac{sin(51^o)}{36.87}{40}](https://tex.z-dn.net/?f=sin%28B%29%3D%5Cfrac%7Bsin%2851%5Eo%29%7D%7B36.87%7D%7B40%7D)
![B=sin^{-1}(\frac{sin(51^o)}{36.87}{40})=57.47^o](https://tex.z-dn.net/?f=B%3Dsin%5E%7B-1%7D%28%5Cfrac%7Bsin%2851%5Eo%29%7D%7B36.87%7D%7B40%7D%29%3D57.47%5Eo)
step 3
Find the measure of angle C
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
![A+B+C=180^o](https://tex.z-dn.net/?f=A%2BB%2BC%3D180%5Eo)
substitute the given values
![51^o+57.47^o+C=180^o](https://tex.z-dn.net/?f=51%5Eo%2B57.47%5Eo%2BC%3D180%5Eo)
![108.47^o+C=180^o](https://tex.z-dn.net/?f=108.47%5Eo%2BC%3D180%5Eo)
![C=180^o-108.47^o=71.53^o](https://tex.z-dn.net/?f=C%3D180%5Eo-108.47%5Eo%3D71.53%5Eo)
I had these kind of questions in my exams recently.... hope this helps Xx
Twice a certain number is tripled:
2 * x * 3 = 6 x ( or : ( 2 x ) * 3 )
Answer: C ) ( 2 x ) 3
Uhh ive had this before but i don’t remember if i got it right
A = (-7,-6)
B = (8,-9)
Find the slope of line AB
m = (y2-y1)/(x2-x1)
m = (-9-(-6))/(8-(-7))
m = (-9+6)/(8+7)
m = -3/15
m = -1/5
The slope of line AB is -1/5.
Flip the fraction and the sign to go from -1/5 to +5/1 = 5. The perpendicular slope is 5.
Let m = 5.
Use the coordinates of point C (2,12) along with the perpendicular slope to get
y - y1 = m(x - x1)
y - 12 = 5(x - 2)
y - 12 = 5x - 10
y = 5x - 10+12
y = 5x + 2
Lastly, convert this to standard form
y = 5x + 2
5x+2 = y
5x+2-y = 0
5x-y = -2
Choice A is the closest match, but the -56 should be -2 instead. It seems like your teacher made a typo somewhere.