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:
-10
Step-by-step explanation:
3-13=-10
50% chance they will land on the same number and there’s also a 50% chance they won’t.
Answer:
The square is the next step
Step-by-step explanation:
Answer:
(D) is the right answer
Step-by-step explanation:
The cross section will be a quadrilateral when the intersecting plane forms a closed four sided polygon along with the pyramid.
A triangular pyramid has four faces. So, to form four straight lines and therefore a quadrilateral, the intersecting plane must intersect all four faces.
A. In this case the plane will only intersect one side of the pyramid so four sided polygon can't be formed.
B. It will only intersect the two sides of the pyramid but the cross section will not be a quadrilateral.
C. In this case the plane will intersect three sides of the pyramid so the cross section will be a triangle not a quadrilateral.
D. In this case the plane intersects all the four faces forming a closed polygon of 4 straight lines so the cross section will be a quadrilateral.
So, the Correct Option is (D) : When the plane intersects the base and all three lateral faces of the pyramid, the cross section of the triangular pyramid will be a quadrilateral.
