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Tems11 [23]
2 years ago
13

Find the missing side or angle. Round to the nearest tenth.

Mathematics
1 answer:
BartSMP [9]2 years ago
8 0

Answer:

b = 2.7

Step-by-step explanation:

Given:

< C = 53°

< B = 80°

a = 2

Required:

Find b

Solution:

The question given suggests we are given measures for a ∆.

To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.

=> A = 180 - (53 + 80) = 47°

Law of Sines: \frac{a}{sin(A} = \frac{b}{sin(B}

Plug in the values into the formula

\frac{2}{sin(47} = \frac{b}{sin(80}

Cross multiply

2*sin(80) = b*sin(47)

Divide both sides by sin(47) to make b the subject of formula

\frac{2*sin(80)}{sin(47} = b

2.69 = b

b = 2.7 (nearest tenth)

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Step-by-step explanation:

We are given the following data;

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       32                     32 - 46 = -14                      196

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       41                      41 - 46 = -5                         25

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       44                     44 - 46 = -2                          4

       45                     45 - 46 = -1                           1

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       55                      55 - 46 = 9                        81

      59                       59 - 46 = 13                      169

       61                       61 - 46 = 15                       225

       63                       63 - 46 = 17                      289

       66                       66 - 46 = 20                <u>     400    </u>    

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Firstly we will calculate Mean, Xbar = \frac{\sum X}{n}

  Xbar = \frac{20+ 23+ 32+ 36+ 41+ 43+ 44+ 45+ 47+ 54+ 55+ 59+ 61+ 63+ 66}{15} = 45.93 ≈ 46

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