C^2 = a^2 + b^2 - 2ab cos C make cos C the subject of the formula

=cos C

Step-by-step explanation:

Start with the parts that are more loosely attached to the cos C: the a² and the b², they are only attached with addition, which can be easily undone by subtracting from both sides. That gives you c²-a²-b²=-2abC

Next, since you want to isolate cosC, you will want to divide by everything attached to the cosC by multiplication: (c²-a²-b²)÷(-2ab)=cosC. Then you can neaten it up and put it in fraction form: =cos C

0.85 or 85%

step-by-step explanation:

1) divide 23 by 27

2) round the decimal to the nearest 10

3) so your answer would be 0.85 or 85%

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.