PLEASE HELP!! Solve the triangle

Option D. m<A = 43, m<B = 55, a = 20

Step-by-step explanation:

1. Determination of angle B.

Angle C = 82

Opposite C (c) = 29

Opposite B (b) = 24

Angle B =?

Using Sine rule, we can obtain the value of angle B as follow:

b/Sine B= c/Sine C

24/Sine B = 29/Sine 82

Cross multiply

29 × Sine B = 24 × Sine 82

Divide both side by 29

Sine B = (24 × Sine 82) /29

Sine B = 0.8195

Take the inverse of Sine.

B = Sine¯¹ (0.8195)

B = 55

2. Determination of angle A.

Angle C = 82

Angle B = 55

Angle A =?

The value of angle A can be obtained as follow:

A + B + C = 180 (sum of angle in a triangle)

A + 55 + 82 = 180

A + 137 = 180

Collect like terms

A = 180 – 137

A = 43

3. Determination of side a (Opposite A)

Angle C = 82

Opposite C (c) = 29

Angle A = 43

Opposite A (a) =?

The value 'a' can be obtained as by using sine rule as illustrated below:

a/Sine A = c/Sine C

a/Sine 43 = 29/Sine 82

Cross multiply

a × Sine 82 = 29 × Sine 43

Divide both side by Sine 82

a = (29 × Sine 43) /Sine 82

a = 20

Therefore,

m<A = 43, m<B = 55, a = 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.

536

step-by-step explanation: