Answer:
See explanation
Step-by-step explanation:
Use trigonometric functions definitions:
[tex]\cos \theta =\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}\\ \\\sin \theta =\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}\\ \\\tan \theta =\dfrac{\text{Opposite leg}}{\text{Adjacent leg}}[/tex]
1. Using the definition,
[tex]\sin A=\dfrac{5}{13}\\ \\\cos A=\dfrac{12}{13}\\ \\\tan A=\dfrac{5}{12}\\ \\\sin C=\dfrac{12}{13}\\ \\\cos C=\dfrac{5}{13}\\ \\\tan C=\dfrac{12}{5}[/tex]
2. By the Pythagorean theorem,
[tex]WX^2=XY^2+YW^2\\ \\WX^2=12^2+9^2=144+81=225\\ \\WX=15[/tex]
Using the definition,
[tex]\sin W=\dfrac{12}{15}=\dfrac{4}{5}\\ \\\cos W=\dfrac{9}{15}=\dfrac{3}{5}\\ \\\tan W=\dfrac{12}{9}=\dfrac{4}{3}\\ \\\sin X=\dfrac{9}{15}=\dfrac{3}{5}\\ \\\cos X=\dfrac{12}{15}=\dfrac{4}{5}\\ \\\tan X=\dfrac{9}{12}=\dfrac{3}{4}[/tex]
3. By the Pythagorean theorem,
[tex]ML^2=ME^2+EL^2\\ \\34^2=16^2+ME^2\\ \\ME^2=34^2-16^2=(34-16)(34+16)=18\cdot 50=900\\ \\ME=30[/tex]
Using the definition,
[tex]\sin L=\dfrac{30}{34}=\dfrac{15}{17}\\ \\cos L=\dfrac{16}{34}=\dfrac{8}{17}\\ \\\tan L=\dfrac{30}{16}=\dfrac{15}{8}\\ \\\sin M=\dfrac{16}{34}=\dfrac{8}{17}\\ \\cos M=\dfrac{30}{34}=\dfrac{15}{17}\\ \\\tan M=\dfrac{16}{30}=\dfrac{8}{15}[/tex]
