1. Find the length a.
13
11
108°
с
а
B

a = 19.451838 ≈ 20

Step-by-step explanation:

==>Given:

∆ABC with,

<A = 108°

AB = c = 11

AC = b = 13

BC = a = ?

==>Required:

Length of a

==>Solution:

Given 2 sides and a measure of 1 angle, let's find the length of a using the Cosine rule:

a² = b² + c² – 2bc cos(A)

Where a = ?

b = 13

c = 11

A = 108°

Thus,

a² = 13² + 11²- 2(13 × 11) × cos(108)

a² = 169 + 121 - 2(143) × cos(108)

a² = 290 - 286 × (-0.3090)

a² = 290 + 88.374

a² = 378.374

a = √378.374

a = 19.451838 ≈ 20

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.

answer: 193

explanation:

200-7 = 193