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algol [13]
3 years ago
8

HELP PLSFind all the missing elements:

Mathematics
1 answer:
bezimeni [28]3 years ago
6 0

Answer:

a = 6.7 , c = 2.0

Step-by-step explanation:

<h3><u>For side a</u></h3>

To find the missing side a we use the sine rule

<h3>\frac{ |b| }{ \sin(B) }  =  \frac{ |a| }{ \sin(A) }</h3>

From the question

B = 58°

b = 6

A = 109°

Substituting the values into the above formula we have

<h3>\frac{6}{ \sin(58) }  =  \frac{ |a| }{ \sin(109) }</h3>

<h3>|a|  \sin(58)  =  6\sin(109)</h3>

Divide both sides by sin 58°

<h3>|a|  =  \frac{6 \sin(108) }{ \sin(58) }</h3>

a = 6.728791

<h3>a = 6.7 to the nearest tenth</h3>

<h3><u>For side c</u></h3>

To find side c we use the sine rule

That's

<h3>\frac{ |b| }{ \sin(B) }  =  \frac{ |c| }{ \sin(C) }</h3>

C = 13°

<h3>\frac{6}{ \sin(58) }  =  \frac{ |c| }{ \sin(13) }</h3>

<h3>|c|  \sin(58)  = 6 \sin(13)</h3>

Divide both sides by sin 58°

<h3>|c|  =  \frac{6 \sin(13) }{ \sin(58) }</h3>

c = 1.591544

<h3>c = 2.0 to the nearest tenth</h3>

Hope this helps you

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