CPhill

The geometric mean of n values equals the nth root their product

So we have

²√[8 * 12 ]  =

²√[96 ]  = 

²√[16 * 6] = 

4√6 

We have an opposite side and an adjacent side......therefore......

tanθ  = (36 - 5.5) / 50   =  30.5 / 50

So, the angle is given by

tan^-1 (30.5 / 50 ) = θ = about 31.4°

Here you go.....

We know an angle and an adjacent side, and we're trying toi find the hypotenuse (the ramp length)  ....the cosine seems the natural choice, here.....so we have

cos13° = 25/ h     rearrange

h = 25 / cos 13°  = about 25.7 ft

This system has no solution....if we subtracted the second equation from the first, we obtain

0 = 9

Since this is impossible.....no solution exists

If the exterior angle is 30, the interior angle is supplementary to this = 150 

And we have

(n -  2)(180) / n = 150

(n - 2)(180) = 150n

180n - 360  = 150n   rearrange

30n = 360      divide by 30 on both sides

n = 12 sides  {a dodecagon}

Let the width  = W

Then the length is 2W

And L x W x H  = Volume

So we have

2W x W x 3 = 420    simplify

6W^2  = 420        divide both sides by 6

W^2  = 70            take the square root of both sides

W = √70 ft = about 8.4 ft

Note that the y values are the same.....this indicates a horizontal line....

The mean is given by the sum of the values / the number of values  ......so we have...

[25 + 10 + 40 ] /  3  =

75 / 3  =

25