Can someone me, i need to know the missing side length (x) using trigonometric ratios.

x=6/cos(72) is the exact answer.

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Step-by-step explanation:

Sine

opposite

hypotenuse

Cosine

adjacent

hypotenuse

Tangent

opposite

adjacent

Soh Cah Toa is an abbreviation used to help remember the trigonometric ratios.

We see we have the angle measurement 72 degrees given at the bottom. I'm going to label my sides with respect to that angle.

The hypotenuse is x.

The adjacent is 6.

We don't have anything about the opposite side but we don't need it to find x.

So anyways we have this:

The hypotenuse is x and

the adjacent is 6.

If you look at the ratios we want to use cosine.

or

We are going to cross multiply.

x cos(72)=1 (6)

cos(72) * x=6

Now we are going to divide both sides by cos(72) giving us:

x=6/cos(72)

x=6/cos(72) is the exact answer.

Let's put it into our calculator now:

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∠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.

answer:

a=9

step-by-step explanation: lmk if you need a explanation