Mathematics, 30.07.2019 16:20 erickasmith1988

If the sine of an angle equals to {2}/{5}, then the tangent of the angle could be:
1. sqrt(21)/2
2. 5/2
3. 2/sqrt(29)
4. sqrt(29)/2
5. 2/sqrt(21)

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Answer from: bartam833oz4qy6

If the sine of an angle equals to {2}/{5}, then the tangent of the angle could be:

5. $\frac{2}{\sqrt{21} }$

Step-by-step explanation:

Imagine a triangleThe sine of an angle is equal to the length of the opposite leg over the hypotenuse. HINT: SOHCAHTOA

To find the adjacent leg (a):

Using the pythagorean theorem: $a^{2} + b^{2} =c^{2}$

- a and b are the lenght of the sides and c is the hypotenuse

we know one side and the hypotenuse. Therefore plugging into the formula we get:

$a^{2} + 2^{2} =5^{2}$

where a is the adjacent leg of the triangle, solving for a we get:

$a^{2} =5^{2}- 2^{2}$

$a^{2} = 21$

$a = \sqrt{21}$

To find the tangent of the angle:

Since tangent is opposite leg over the adjacent leg:

tan θ = $\frac{2}{\sqrt{21} }$

Answer from: Quest

∠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 from: Quest

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

Which are the possible side lengths of a triangle?

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If the sine of an angle equals to {2}/{5}, then the tangent of the angle could be:
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