The distance between the building and the base of the ladder is 5√3 feet.
<u>Step-by-step explanation</u>:
<u>Consider a right angle triangle</u>,
- Hypotenuse = Paula leaned a 10 ft ladder against a building.
- Height = the top of the ladder is exactly 5 feet up in the building.
- Base = 'x' ft, distance between the building and the base of the ladder.
<u>From the Pythagorean theorem</u>,
Base, x = 
⇒ x = 
⇒ x = 
⇒ x = 
⇒ x = 5√3
The distance between the building and the base of the ladder is 5√3 feet.
The answer is 16!!!!!! If you need me to explain I shall
Answer: 1440
Step-by-step explanation:
To arrange 3 boys and 4 girls such that no two boys are together.
Since boys should be arranged between the girls.
So first arrange the girls.
Assume that the girls are placed, then there will be 5 spaces left for 3 boys.
The number of combinations to fill these places = 
Also, 3 boys can arrange themselves in 3! =3 x 2 x 1 = 6 ways
4 girls can arrange themselves in 4! = 4x 3 x 2 x 1 = 24 ways
Then, the total number of arrangements = 10 x 6 x 24 = 1440
Hence, the required number of arrangements = 1440
