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Here is a triangle. Find cos(A), sin(A), and tan(A). Explain your reasoning.

Here Is A Triangle Find CosA SinA And TanA Explain Your Reasoning class=

Sagot :

Answer:

[tex]\cos(A)=\dfrac{3\sqrt{10}}{10}[/tex]

[tex]\sin(A)=\dfrac{\sqrt{10}}{10}[/tex]

[tex]\tan(A)=\dfrac13[/tex]

Step-by-step explanation:

Calculate the hypotenuse of ΔABC using Pythagoras' Theorem:  [tex]a^2+b^2=c^2[/tex]  (where a and b are the legs and c is the hypotenuse of a right triangle)

Given:

  • a = 2
  • b = 6

[tex]\implies 2^2+6^2=c^2\\\\\implies 4 + 36 = c^2\\\\\implies c^2=40\\\\\implies c=\sqrt{40} \\\\\implies c=2\sqrt{10}[/tex]

Trig ratios:

[tex]\sin(\theta)=\dfrac{O}{H} \ \ \ \ \cos(\theta)=\dfrac{A}{H} \ \ \ \ \tan(\theta)=\dfrac{O}{A}[/tex]

where [tex]\theta[/tex] is the angle, O is the side opposite the angle, A is the side adjacent the angle, H is the hypotenuse in a right triangle.

[tex]\cos(A)=\dfrac{6}{2\sqrt{10} }=\dfrac{3\sqrt{10}}{10}[/tex]

[tex]\sin(A)=\dfrac{2}{2\sqrt{10} }=\dfrac{\sqrt{10}}{10}[/tex]

[tex]\tan(A)=\dfrac{2}{6}=\dfrac13[/tex]

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