Answer: A. [tex]\cos L=\frac{5}{13}[/tex]
Step-by-step explanation:
For angle y in a right triangle ,the trigonometric ratio of cos y is given by :-
[tex]\cos y=\frac{\text{side adjacent to y}}{\text{Hypotenuse}}[/tex]
Given: The side adjacent to angle L= 5 units
The side opposite to angle L = 12 units
Let h be the hypotenuse, then using Pythagoras in the given right triangle, we get
[tex]h^2=12^2+5^2\\\\\Rightarrow\ h^2=144+25\\\\\Rightarrow\ h^2=169\\\\\Rightarrow\ h=\sqrt{169}=13[/tex]
Thus, hypotenuse = 13 units
Now, the trigonometric ratio for cos L is given by :-
[tex]\cos L=\frac{\text{side adjacent to L}}{\text{Hypotenuse}}\\\\\Rightarrow\cos L=\frac{5}{13}=\frac{5}{13}[/tex]
Hence, the value of cos L =[tex]\frac{5}{13}[/tex]
