In ΔABC, ∠A measures 132° and the values of b and a are 36 and 70, respectively. Find the remaining measurements of the triangle, and round your answers to the nearest tenth. ∠B = 82.2°, ∠C = 62.8°, c = 40.6 ∠B = 82.2°, ∠C = 62.8°, c = 30 ∠B = 22.5°, ∠C = 25.5°, c = 40.6 ∠B = 22.5°, ∠C = 25.5°, c = 30

The correct answer is (C) Angle B = 22.5, Angle C = 25.5 and line c = 40.6

Step-by-step explanation: Please refer to the attached diagram for details.

The triangle has been given with angle A measuring 132 degrees and line a measuring 70 units. Angle B is not given but line b measures 36 units. We can apply the sine rule which states that;

a/SinA = b/SinB = c/SinC

Hence, we now have

70/Sin132 = 36/SinB

By cross multiplication we now have

70 (SinB) = 36 (Sin132)

SinB = {36 (Sin132)}/70

SinB = (36 x 0.7432)/70

SinB = 0.3822

By use of calculator or table of values,

B = 22.5 degrees.

To calculate angle C,

Angle C = 180 - (132 + 22.5)

{Sum of angles in a triangle equals 180}

C = 180 - 154.5

C = 25.5 degrees

To calculate line C, having derived angle C,

70/Sin132 = c/Sin25.5

By cross multiplication we now have

70 (Sin25.5) = c (Sin132)

70 x 0.4305 = c x 0.7432

(70 x 0.4305)/0.7432 = c

40.55 = c

c is approximately 40.6

Therefore, Angle B = 22.5, Angle C = 25.5, and line c = 40.6

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.