[Ne] 3s^2 3p^2. is the correct answer :)
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)
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Question thirteen is a right angle (because if you plot the pints, it obviously looks like a fit angle)
Question fourteen is c ( because when you plot all the points, the first two options don't make sense if side pq is congruent to qr, then we are left with options c and d. Option d forms a right triangle (and sides pq and qr can't be congruent) . Whereas in option c, it is mathematically possible for pq and qr to be congruent to one another)
Basically, all you have to do is plot the points for both questions and the answer will become obvious)