Trigonometric functions are the ratio of different sides of a triangle. The ratios sin∠m, cos∠m, and Tan∠m are 0.758, 0.6522, and 1.1624.
What are Trigonometric functions?
The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\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.
As it is given that the base of the triangle for the ∠m is Mk(15 units), the perpendicular is KL(4√19), and the hypotenuse is 23. Now, the trigonometric ratios can be written as,
Sine
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\\rm Sin (\angle m)=\dfrac{KL}{ML}\\\\\\\rm Sin (\angle m)=\dfrac{4\sqrt{19}}{23}\\\\\\\rm Sin (\angle m)=0.758069\approx 0.758[/tex]
Cosine
[tex]\rm Cos\theta=\dfrac{Base}{Hypotenuse}\\\\\\\rm Cos(\angle m)=\dfrac{MK}{ML}\\\\\\\rm Cos(\angle m)=\dfrac{15}{23}\\\\\\\rm Cos (\angle m)=0.65217\approx 0.6522[/tex]
Tangent
[tex]\rm Tan\theta=\dfrac{Perpendicular}{Base}\\\\\\\rm Tan(\angle m)=\dfrac{KL}{MK}\\\\\\\rm Tan(\angle m)=\dfrac{4\sqrt{19}}{15}\\\\\\\rm Tan(\angle m)=1.16237\approx 1.1624[/tex]
Hence, the ratios sin m, cos m, and tan m are 0.758, 0.6522, and 1.1624.
Learn more about Trigonometric functions:
https://brainly.com/question/6904750
