Question

(GEOMETRY HELP) Given right triangle JKL, what is the value of cos(L)?
A. 5/13
B. 5/12
C. 12/13
D. 12/5

Answer 1

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

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

Answer 2

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:

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