Respuesta :

calculista

Step 1

In the right triangle JKL

Find the value of JL

Applying the Pythagorean Theorem

[tex]JL^{2} =JK^{2}+KL^{2}[/tex]

in this problem we have

[tex]JK=12\ units\\KL=5\ units[/tex]

substitute the values

[tex]JL^{2} =12^{2}+5^{2}[/tex]

[tex]JL^{2} =169[/tex]

[tex]JL=13\ units[/tex]

Step 2

Find the value of cos(L)

we know that

[tex]cos(L)=\frac{adjacent\ side\ angle\ L}{hypotenuse}=\frac{KL}{JL}=\frac{5}{13}[/tex]

therefore

the answer is the option A

[tex]cos(L)=\frac{5}{13}[/tex]

To solve the problem we must know about trigonometric functions.

The value of Cos(∠L) is [tex]\dfrac{5}{13}[/tex].

What are Trigonometric functions?

[tex]Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]Tan\theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Given to us

  • JK = 12
  • KL = 5

What is Hypotenuse?

Thy hypotenuse is the largest side of a right-angle triangle. such that the square of the hypotenuse is equal to the sum of the squared values of the other two sides.

[tex](Hypotenuse)^2 = (Base)^2 + (Altitude^2)[/tex]

What is the length of the hypotenuse?

The length of the hypotenuse can be given using the Pythagoras theorem. therefore,

[tex](Hypotenuse)^2 = (Base)^2 + (Altitude^2)[/tex]

[tex](JL)^2 = (JK)^2+(KL)^2\\(JL)^2 = 12^2 +5^2\\(JL)^2 = 144 +25\\(JL) = \sqrt{169} = 13[/tex]

What is Cos(∠L)?

We know that cos is the ratio of base and hypotenuse of the triangle. therefore,

[tex]Cos(\theta)=\dfrac{Base}{Hypotenuse}[/tex]

Substituting the values we get,

[tex]Co(\angle L)=\dfrac{KL}{JL}\\\\Co(\angle L)=\dfrac{5}{13}\\[/tex]

Hence, the value of Cos(∠L) is [tex]\dfrac{5}{13}[/tex].

Learn more about Trigonometric functions:

https://brainly.com/question/15706158

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