In triangle xyz,sin x=5/13. Find the tan x?
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To find the value of tan(x) in triangle XYZ, where sin(x) = 5/13, we can use the relationship between the trigonometric functions sine, cosine, and tangent.
Tangent is defined as the ratio of sine to cosine.
We know that sin(x) = opposite / hypotenuse. In this case, sin(x) = 5/13, which means that the side opposite angle x has a length of 5 and the hypotenuse has a length of 13.
To find the side adjacent to angle x, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's assume the adjacent side has a length of a.
Using the Pythagorean theorem:
a^2 + 5^2 = 13^2
a^2 + 25 = 169
a^2 = 169 - 25
a^2 = 144
a = sqrt(144)
a = 12
Now that we know the lengths of the opposite and adjacent sides (5 and 12 respectively), we can find the value of tan(x) using the definition mentioned earlier:
tan(x) = opposite / adjacent
tan(x) = 5 / 12
So, the value of tan(x) in triangle XYZ is 5/12.