A ladder needs to reach a second-story window that is 13 feet above the ground and make an angle with the ground of 72°. How far out from the building does the base of the ladder need to be positioned? Round your answer to the nearest tenth.

Step-by-step explanation:

The set up will form a right angled triangle as shown in the attachment

The length of the ladder is the hypotenuse of the triangle = 13ft

The distance between the building and the base of the ladder will be the adjacent of the triangle. Using the SOH,CAH, TOA trigonometry identity to  determine how far out from the building the base of the ladder need to be positioned.

According to CAH;

Cosβ = Adjacent/Hypotenuse

β is the angle that the ladder makes with the ground

cos72° = Adjacent/13

Adjacent = 13cos72°

Adjacent = 4.0 feet (to the nearest tenth)

The base of the ladder need to be positioned 4.0 feet out from the building

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

the answer is c. 23/3