Answer:
B
Step-by-step explanation:
Use the Pythagorean theorem for the right triangle ABC:
[tex]AC^2+BC^2=AB^2,\\ \\AC^2=15^2-12^2,\\ \\AC^2=225-144,\\ \\AC^2=81,\\ \\AC=9\ cm.[/tex]
By the definition,
[tex]\cos A=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{AC}{AB}=\dfrac{9}{15}=\dfrac{3}{5},\\ \\\sin A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}=\dfrac{12}{15}=\dfrac{4}{5},\\ \\\sec A=\dfrac{1}{\cos A}=\dfrac{1}{\frac{3}{5}}=\dfrac{5}{3},\\ \\\csc A=\dfrac{1}{\sin A}=\dfrac{1}{\frac{4}{5}}=\dfrac{5}{4},\\ \\\tan A=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{BC}{AC}=\dfrac{12}{9}=\dfrac{4}{3},\\ \\\cot A=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{AC}{BC}=\dfrac{9}{12}=\dfrac{3}{4}.\\ \\[/tex]
