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Verified Answer :

calculista

Step 1

In the right triangle JKL

Find the value of JL

Applying the Pythagorean Theorem

\(JL^{2} =JK^{2}+KL^{2}\)

in this problem we have

\(JK=12\ units\\KL=5\ units\)

substitute the values

\(JL^{2} =12^{2}+5^{2}\)

\(JL^{2} =169\)

\(JL=13\ units\)

Step 2

Find the value of cos(L)

we know that

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

therefore

the answer is the option A

\(cos(L)=\frac{5}{13}\)

To solve the problem we must know about trigonometric functions.

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

What are Trigonometric functions?

\(Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\)

\(Cos \theta=\dfrac{Base}{Hypotenuse}\)

\(Tan\theta=\dfrac{Perpendicular}{Base}\)

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.

\((Hypotenuse)^2 = (Base)^2 + (Altitude^2)\)

What is the length of the hypotenuse?

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

\((Hypotenuse)^2 = (Base)^2 + (Altitude^2)\)

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

What is Cos(∠L)?

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

\(Cos(\theta)=\dfrac{Base}{Hypotenuse}\)

Substituting the values we get,

\(Co(\angle L)=\dfrac{KL}{JL}\\\\Co(\angle L)=\dfrac{5}{13}\\\)

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

Learn more about Trigonometric functions:

https://brainly.com/question/15706158

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