Answer:
a. x=1
b. x=18/5
Step-by-step explanation:
Check the picture below to the left, let's use those sides with the law of sines
![\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(14^o)}{97}=\cfrac{sin(84^o)}{XZ}\implies XZ = \cfrac{97\cdot sin(84^o)}{sin(14^o)}\implies XZ \approx 398.76 \\\\\\ \stackrel{\textit{now using SOH CAH TOA}}{cos(82^o) = \cfrac{XW}{XZ}}\implies XZcos(82^o)=XW \\\\\\ 398.76cos(82^o)\approx XW\implies 55.497\approx XW\implies \stackrel{\textit{rounded up}}{55=XW}](https://tex.z-dn.net/?f=%5Ctextit%7BLaw%20of%20sines%7D%20%5C%5C%5C%5C%20%5Ccfrac%7Bsin%28%5Cmeasuredangle%20A%29%7D%7Ba%7D%3D%5Ccfrac%7Bsin%28%5Cmeasuredangle%20B%29%7D%7Bb%7D%3D%5Ccfrac%7Bsin%28%5Cmeasuredangle%20C%29%7D%7Bc%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7Bsin%2814%5Eo%29%7D%7B97%7D%3D%5Ccfrac%7Bsin%2884%5Eo%29%7D%7BXZ%7D%5Cimplies%20XZ%20%3D%20%5Ccfrac%7B97%5Ccdot%20sin%2884%5Eo%29%7D%7Bsin%2814%5Eo%29%7D%5Cimplies%20XZ%20%5Capprox%20398.76%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bnow%20using%20SOH%20CAH%20TOA%7D%7D%7Bcos%2882%5Eo%29%20%3D%20%5Ccfrac%7BXW%7D%7BXZ%7D%7D%5Cimplies%20XZcos%2882%5Eo%29%3DXW%20%5C%5C%5C%5C%5C%5C%20398.76cos%2882%5Eo%29%5Capprox%20XW%5Cimplies%2055.497%5Capprox%20XW%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Brounded%20up%7D%7D%7B55%3DXW%7D)
Answer:
12°
Step-by-step explanation:
a right triangle implies there is an angle that is 90°
another angle is 78°
the third angle is 180 - (90 + 78) = 180 - 168 = 12°
<span>M can have a coordinate of (-9) or (1)
There are potentially 3 different places for point M to go. It can be placed to the left of point A, between points A and B, and to the right of point B. Let's check those three possibilities.
1. Left of point A. This works if the distance between M and A is the same as the distance between A and B. So
distance between A and B = 6 - (-1.5) = 6 + 1.5 = 7.5
So the location for M would be
-1.5 - 7.5 = -9
So point M can have the value of -9.
2. Between A and B.
This would also work. Since we want a 1:2 ratio, place M one third of the way from A to B. Since we already know the distance between A and B to be 7.5, that means that we should add 7.5/3 = 2.5 to the value of A. So
-1.5 + 2.5 = 1
So point M can also have the value of 1.
3. To the right of point B
This won't work. Point B will always be closer to M than point A will be. So it's impossible to get a ratio of 1:2.</span>
