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kupik [55]
3 years ago
6

Solve the following triangle in which given sides are a=7 b=7 c=9

Mathematics
1 answer:
blagie [28]3 years ago
8 0
We have an isosceles triangle;
A=opposite angle side a.
B=opposite angle side b.
C=opposite angle side c.

A=B
Method 1:

We can divide the isosceles triangle in two right triangles,
hypotenuse=7
side=9/2=4.5

B=A=arccossine (4.5/7)=49.994799...º≈50º
C/2=90º-50º=40º  ⇒ C=2*40º=80º

Answer:
a=7;  A=50º
b=7;  B=50º
<span>c=9;  C=80º

Method 2:
Law of cosines:
a²=b²+c²-2bcCosA  ⇒CosA=(a²-b²-c²)/(-2bc)
CosA=(49-49-81) / (-126)=0.642857
A=arco cos (81/126)≈50º

B=A=50º

A+B+C=180º
50º+50º+C=180º
C=180º-100º
C=80º

Answer:

</span>a=7;  A=50º
b=7;  B=50º
<span>c=9;  C=80º</span>

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