CPhill

I think the  question might be this...

6 * (2 + 1/5)  = 6 (11/5) = 66/5 = 13 + 1/5

It's makes more sense to find the hypoteneuse, first.

The length of the hypoteneuse is = Sqrt(12^2 + 5^2) = 13 inches

Thus, a square drawn on the hypoteneuse will have an area of 13^2 = 169 sq. inches

BTW......the side lengths of 5 - 12 - 13 are known as a "Pythagorean Triple." There are an infinite number of these "triples.'

Simplifying the left side, we have

8.55 + M = 124/87     Subtract 8.55 from both sides

M = (124/87 - 8.55)     ≈ -7.125

The experimental probability of the spinner "landing in q"....also kwown as the empirical probabilty....is 4/15

The theoretical probability is just 3/15.......since we expect that the spinner will land in any area 1/5 of the time.....then it should land in each area an equal number of times (once) in any five spins.

The "theoretical" probability is what we expect to happen......the "experimental" probabilty is what actually does happen.

BTW.......as the number of spins increase to some "large number" the empirical probability tends toward the theoretical probabiity.

It depends upon which side you're missing

If it's the hypoteneuse (the side opposite the right angle), we just square each of the other two known sides, add these together,  and then take the square root of this sum....that's the hypoteneuse

If it's any other side, we square both of the other two known sides, and subtract the smaller square from the larger, and take the square root of that difference. That's the length of the missing side (called a "leg").

The side opposite the 30 degree angle will be (1/2) as long as the hypoteneuse ... (9ft)

The side opposite the 60 degree angle will be (√3/2)  times as long as the hypoteneuse =

18* √3/2 = (9√3) ft

So the perimeter is (18 + 9 + 9√3) = (27 + 9√3) = 9(3 + √3) ft.

If it's a half sphere and it's 15 ft, wide....the radius must be 7.5 ft.

The floor area is just the area of a circle with a radius of 7.5 ft. =

Floor Area = pi * (7.5)^2.......I'll let you evaluate that.....BTW...the answer is in square feet !!

The inside height of the igloo is also 7.5 ft.........if the exact center of the floor is the center of the half-sphere.....then the radius from that point to the top of the igloo is just 7.5 ft.....

Of course...if we want to be technically correct....we need to add the 8 inch thick ice block to obtain the "outside" height!!

Using the sine inverse, we have

asin (31/42) ≈ 47.57°

Be aware that this might be a 47.57° angle in the second quadrant, i.e. ≈ 132.43°

Use the on-site calculator............I believe it's still working just fine.....

-3^2 = -(3)^2 = -9

Be careful, this isn't the same as (-3)^2 = (-3)(-3) = 9

In the first case, the exponent is applied only on the "3"

In the second case, it's applied on (-3)