Answer: The distance from ship B to the submarine is 1270.68 feet and the distance from ship A to the submarine is 1084.18 feet.
Step-by-step explanation:
Since we have given that
Distance between Ships A and B = 1425 feet
Angle of depression from ship A to the submarine =59°
Angle of depression from ship B to the submarine = 47°
As shown in the figure below:
Remaining angle will be
![180\textdegree-(47\textdegree+59\textdegree)\\\\=180\textdegree-106\textdegree\\\\=74\textdegree](https://tex.z-dn.net/?f=180%5Ctextdegree-%2847%5Ctextdegree%2B59%5Ctextdegree%29%5C%5C%5C%5C%3D180%5Ctextdegree-106%5Ctextdegree%5C%5C%5C%5C%3D74%5Ctextdegree)
So, we will use "Sine formula ":
![\frac{\sin 74\textdegree}{1425}=\frac{\sin 59\textdegree}{B}\\\\B=\frac{1425\times \sin 59\textdegree}{\sin 74\textdegree}\\\\B=1270.68\ feet](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%2074%5Ctextdegree%7D%7B1425%7D%3D%5Cfrac%7B%5Csin%2059%5Ctextdegree%7D%7BB%7D%5C%5C%5C%5CB%3D%5Cfrac%7B1425%5Ctimes%20%5Csin%2059%5Ctextdegree%7D%7B%5Csin%2074%5Ctextdegree%7D%5C%5C%5C%5CB%3D1270.68%5C%20feet)
Similarly,
![\frac{\sin 74\textdegree}{1425}=\frac{\sin 47\textdegree}{A}\\\\A=\frac{1425\times \sin 47\textdegree}{\sin 74\textdegree}\\\\A=1084.18\ feet](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%2074%5Ctextdegree%7D%7B1425%7D%3D%5Cfrac%7B%5Csin%2047%5Ctextdegree%7D%7BA%7D%5C%5C%5C%5CA%3D%5Cfrac%7B1425%5Ctimes%20%5Csin%2047%5Ctextdegree%7D%7B%5Csin%2074%5Ctextdegree%7D%5C%5C%5C%5CA%3D1084.18%5C%20feet)
Hence, the distance from ship B to the submarine is 1270.68 feet and the distance from ship A to the submarine is 1084.18 feet.
Answer:
![3 (a-2) (a-5)](https://tex.z-dn.net/?f=3%20%28a-2%29%20%28a-5%29)
Step-by-step explanation:
The first step is to find the GCF. Here, it's 3.
![3(a^2-7a+10)](https://tex.z-dn.net/?f=3%28a%5E2-7a%2B10%29)
Then, you factor the polynomial in the parenthesis.
To find the factors, you will need to find 2 numbers that add to -7, and multiply to 10. -2 and -5 add to -7 and multiply to 10. Now, replace -7a with the factors.
![a^2-2a-5a+10](https://tex.z-dn.net/?f=a%5E2-2a-5a%2B10)
This of this polynomial as 2 problems.
![-5a+10](https://tex.z-dn.net/?f=-5a%2B10)
Then, factor again.
![-5a+10](https://tex.z-dn.net/?f=-5a%2B10)
![-5(a-5)](https://tex.z-dn.net/?f=-5%28a-5%29)
Then, you keep the factors in parenthesis, and combine the numbers on the outside.
![(a-2)(a-5)(a-5)](https://tex.z-dn.net/?f=%28a-2%29%28a-5%29%28a-5%29)
Since, there are 2 of the same factor, you only need one.
![(a-2)(a-5)](https://tex.z-dn.net/?f=%28a-2%29%28a-5%29)
BUT REMEMBER!! In the very beginning, we had a 3 that we took out, we STILL need to add that to the final answer. The <u>final answer</u> is:
![3 (a-2) (a-5)](https://tex.z-dn.net/?f=3%20%28a-2%29%20%28a-5%29)