In △abc, c=12, m∠b=27°, and a=9. find b.
a. 11.5
b. 13.2
c. 6.8
d. 5.7

Option D is correct.

Step-by-step explanation:

We are given c = 12

m∠B = 27°

a = 9

We need to find b

We would use Law of Cosines

Putting values and solving

So, Option D is correct.

D. 5.7

Step-by-step explanation:

We have been given that in △ABC,c=12, m∠B=27°, and a=9. We are asked to find the value of b.

We will use law of cosines to solve for b.

Upon substituting our given values in law of cosines, we will get:

Now, we will take square root of both sides of our equation.

Therefore, the value of b is 5.7 and option D is the correct choice.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.