Answer:
ZM = 8
WM = 12
XZ = 7
XN = 21
LZ = 20
Step-by-step explanation:
The centroid of a triangle is the point of intersection of the midpoint of the each of the three sides of a triangle. The centroid of a triangle is located inside the triangle and it is known as the center of gravity.
The centroid theorem for a triangle states that the centroid of a triangle is located at 2/3 of the distance from the vertex of the triangle of the middle of the opposite side.
ZM = (2/3)WM (centroid theorem)
Therefore: WZ = (1/3)WM
WM = 3WZ = 3 * 4 = 12
ZM = (2/3) * WM = 2/3 * 12 = 8
ZN = (2/3)XN (centroid theorem)
XN = (3/2)ZN = 3/2 * 14 = 21
XN = 21
XZ + ZN = XN
XZ + 14 = 21
XZ = 7
LZ = (2/3)LY (centroid theorem)
Therefore: ZY = (1/3)LY
LY = 3ZY = 3 * 10 = 30
LZ = (2/3) * LY = 2/3 * 30 = 20
Its a guess and check problem you have to just try to find a combonation of 8 and 10 to get 200
Answer:I think it is 89
Step-by-step explanation:
<span> sin20 * sin40 * sin60 * sin80
since sin 60 = </span><span> √3/2
</span>√3/<span>2 (sin 20 * sin 40 * sin 80)
</span>√3/<span>2 (sin 20) [sin 40 * sin 80]
</span>
Using identity: <span>sin A sin B = (1/2) [ cos(A - B) - cos(A + B) ]
</span>√3/<span>2 (sin 20) (1 / 2) [cos 40 - cos 120]
</span>√3/4<span> (sin 20) [cos 40 + cos 60]
</span>
Since cos 60 = 1/2:
√3/4<span> (sin 20) [cos 40 + (1/2)]
</span>√3/4 (sin 20)(cos 40) + √3/8<span> (sin 20)
</span>
Using identity: <span> sin A cos B = 1/2 [ sin(A + B) + sin(A - B) ]
</span>√<span>3/4 (1 / 2) [sin 60 + sin (-20)] + </span>√3/8<span> (sin 20)
</span>
Since sin 60 = √3/<span>2
</span>√3/8 [√3/2 - sin 20] + √3/8 (sin 20)
3/16 - √3/8 sin 20 + √3/8<span> sin 20
</span>
Cancelling out the 2 terms:
3/16
Therefore, sin20 * sin40 * sin60 * <span>sin80 = 3/16</span>