Find COS Instructions: Find the value of the trigonometric ratio. Make sure to simplify the If needed

Sin X = 12 / 37

Step-by-step explanation:

Given a right angled triangle, we are to obtain the Sin of the angle X ;

Using trigonometry, the sine of the angle X , Sin A is defined as the ratio of the angle opposite X to the hypotenus of the right angle triangle.

In the right angle triangle :

Sin X = opposite / hypotenus

Opposite = 12 ; hypotenus = 37

Sin X = 12 / 37

∠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.

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step-by-step explanation: