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.
perimeter = Answer:
Step-by-step explanation:
5. Perimeter of semi circle = r(pi+2)
Given diameter=17m; r=17/2
Perimeter = (17/2)(pi+2)
6. Given diameter = 10.5
Perimeter = (10.5/2)(pi+2)
Answer:
money : x
in 2 years : x+2
in 5years: x+2= 2800 + 3250
sum= x+2= 6050
x=6050÷2
x=3025
Answer:
-12
Step-by-step explanation:
the opposite of 12 is -12
Answer:
(-4, -2)
Step-by-step explanation:
The x-coordinate would stay the same, but the y-coordinate would be halved. Thus, the corresponding point would be (-4, -2).