Step-by-step explanation:
hope this helps. n=6 or n=9 work is in the attached pic
Answer:
655.36^3, or 281474976.711
Step-by-step explanation:
4 to the power of seven equals 16384.
5 to the power of two equals 25.
Answer: GN runs between a vertex and the midpoint of the opposite side, so it is a median.
HK is an altitude because it is perpendicular to base GJ and H is a vertex.
ML is not perpendicular to a base although it does bisect a base, but anyway, neither M nor L is a vertex: ML is neither altitude nor median.
Step-by-step explanation:
"A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it. ... Each median divides the area of the triangle in half; hence the name" Wikipedia.
<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>
