From the setup of the problem, the "length of the top of the bookcase, measured along the attic ceiling" will be the hypotenuse of a right triangle, the length "AB". We have both the angle between AB and AC and the length of AC (3.24 meters), so we can use trigonometric identities.
The cosine of the 40 degree angle between AB and AC is equivalent to the length of AC divided by the length of AB. Equivalently, we have:
where "h", the hypotenuse, is the length we want. Rearranging the formula to solve for h we have that
which is 4.2295... meters. Converting to centimeters (multiplying by 100) we have that h = 422.95... centimeters, or if we round the value, h = 423 centimeters.
5 Points away could mean it is either (-2, -2) or (-2, -12)
So. The total of the interior angles of a triangle, are equal to 180°. So...add them together, and solve for X.
30x+60=180
30x=120
x=4
The distance adjacent to the smallest angle is the smallest.
Carrie=70°
Nayla=87°
Maria=23°
So...the distance across from Maria.
Carrie and Nayla are closest to each other.
<span>A. 8 wreaths, 6 trees, 2 sleighs
Nothing much to do for this problem except to try each option and see if it meets the constraints of available time. So let's check them out.
A. 8 wreaths, 6 trees, 2 sleighs
prep = 8 * 3 + 6 * 14 + 2 * 4 = 116 hours.
paint = 8 * 2 + 6 * 3 + 2 * 15 = 64 hours.
fire = 8 * 9 + 6 * 4 + 2 * 7 = 110 hours.
All three values are less than or equal to the constraints of 116, 64, and 110.
This option will work.
B. 6 wreaths, 2 trees, 8 sleighs
prep = 6 * 3 + 2 * 14 + 8 * 4 = 78 hours.
paint = 6 * 2 + 2 * 3 + 8 * 15 = 138 hours.
138 is more than the allowed 64, can't do this option.
Don't bother to calculate how many hours of firing needed.
C. 9 wreaths, 7 trees, 3 sleighs
prep = 9 * 3 + 7 * 14 + 3 * 4 = 137 hours.
137 is more than the allowed 116, can't do this option.
Don't bother to calculate how many hours of painting or firing needed.
D. 2 wreaths, 8 trees, 6 sleighs
prep = 2 * 3 + 8 * 14 + 6 * 4 = 142 hours.
142 is more than the allowed 116, can't do this option.
Don't bother to calculate how many hours of painting or firing needed.
Of the 4 choices available, only option "A" falls under the required time constraints.</span>