Answer: [tex]\sin M=\dfrac{12}{13}[/tex]
[tex]\cos M=\dfrac{5}{13}[/tex]
[tex]\tan M=\dfrac{12}{5}[/tex]
Step-by-step explanation:
According to trigonometry , For any angle x in a right triangle we have
[tex]\sin x=\dfrac{\text{Side opposite to x}}{\text{Hypotenuse}}[/tex]
[tex]\cos x=\dfrac{\text{Side adjacent to x}}{\text{Hypotenuse}}[/tex]
[tex]\tan x=\dfrac{\text{Side opposite to x}}{\text{Side adjacent to x}}[/tex]
In the given picture , we have ΔMNL right -angled at N with side length 5 , 12 and 13.
∴ Side ML is hypotenuse [∵Side opposite to right angle is the hypotenuse]
i.e. Hypotenuse = 13
Now, For angle M
Side opposite to ∠M = NL = 12
Side adjacent to ∠M = MN= 5
Then,
[tex]\sin M=\dfrac{12}{13}[/tex]
[tex]\cos M=\dfrac{5}{13}[/tex]
[tex]\tan M=\dfrac{12}{5}[/tex]
