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SSSSS [86.1K]
1 year ago
10

In the triangle shown above m∠B = 114°, m∠C = 22°, and b = 12 in. What is the approximate length of side a? A. 15.78 in B. 9.12

in C. 11.87 in D. 7.39 in
Mathematics
1 answer:
Elena L [17]1 year ago
4 0

The approximate length of side a is 9.12 in. The correct option is B. 9.12 in

<h3>Law of Sines </h3>

From the question, we are to determine the approximate length of side a

From the given information, we have that

m∠B = 114°, m∠C = 22°

Thus,

m∠A = 180° - (114° + 22°)

m∠A = 180° - 136°

m∠A = 44°

Now,

From the law of sines, we have that

a/sinA = b/sinB

Then,

a/sin44° = 12/sin114°

a = (12 ×sin44°)/sin114°

a = 9.12 in

Hence, the approximate length of side a is 9.12 in. The correct option is B. 9.12 in

Learn more on Law of Sines here: brainly.com/question/24138896

#SPJ1

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Answer:

Total surface area of the given figure is 246.75 square mile.

Step-by-step explanation:

Surface Area of the given figure = Lateral surface area + Area of the base

Lateral surface area of the figure = Sum of the areas of 5 triangular surfaces

                                                        = 5(\frac{1}{2} )(\text{Base})(\text{Slant height})

                                                        = \frac{5}{2}(7)(9.3)

                                                        = 162.75 mi²

Surface area of the pentagonal base = 84 mi²

Total surface area of the figure = 162.75 + 84

                                                    = 246.75 mi²

Therefore, total surface area of the given figure is 246.75 square mile.

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