Please help Suppose tan(x) = Two-thirds, and the terminal side of x is located in quadrant I. What is sin(x)?

A.) StartFraction 2 Over StartRoot 13 EndRoot EndFraction
B.) StartFraction 3 Over StartRoot 13 EndRoot EndFraction
C.) Three-halves
D.) StartFraction StartRoot 13 EndRoot Over 2 EndFraction

Please help

Suppose tan(x) = Two-thirds, and the terminal side of x is located in quadrant I.

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Ответ:

robert7248

11.11.2022

Mathematics

$\large\underline{\underline{\red{\sf \blue{\longmapsto} Step-by-step\: Explanation:-}}}$

Given that area of an isosceles triangle is 128m² .

And the triangle is right Angled ∆ .

So , the measure of sides along 90° that is perpendicular and the base will be equal .

Let us say that each of the equal sides is x .

Then , we can find the area of the triangle as ,

$\boxed{\bf{\red{ Area_{triangle}=\dfrac{1}{2}\times(base)\times(height)}}}$

Now , here substitute the respective values ,

$\implies \sf \dfrac{1}{2}\times(base)\times(height)=128m^2$

$\sf\implies \dfrac{1}{2}\times x \times x = 128m^2$

$\sf \implies \dfrac{x^2}{2}=128m^2$

$\sf\implies x^2=128\times2 m^2$

$\sf\implies x^2=256 m^2$

$\sf\implies x=\sqrt{256m^2}$

$\underline{\boxed{\red{\sf\longmapsto x=16m}}}$

Hence the value of value of identical side of the triangle is 16m .

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