Given:
The triangle ABC is a right triangle.
The length of AC = 25, the length of AB = 7 and the length of BC = 24
We need to determine the ratios of sin C, cos C and tan C.
Ratio of sin C:
Using the trigonometric ratio, the ratio of sin C is given by
[tex]sin \ C=\frac{opp}{hyp}[/tex]
where [tex]opp=AB[/tex] and [tex]hyp=AC[/tex]
Thus, we get;
[tex]sin \ C=\frac{AB}{AC}[/tex]
Substituting the values, we get;
[tex]sin \ C=\frac{7}{25}[/tex]
Thus, the ratio of sin C is [tex]\frac{7}{25}[/tex]
Ratio of cos C:
The ratio of cos C can be determined using the trigonometric ratio.
Thus, we have;
[tex]cos C=\frac{adj}{hyp}[/tex]
where [tex]adj=BC[/tex] and [tex]hyp=AC[/tex]
[tex]cos \ C=\frac{BC}{AC}[/tex]
Substituting the values, we get;
[tex]cos \ C=\frac{24}{25}[/tex]
Thus, the ratio of cos C is [tex]\frac{24}{25}[/tex]
Ratio of tan C:
The ratio of tan C can be determined using the trigonometric ratio.
Thus, we have;
[tex]tan \ C=\frac{opp}{adj}[/tex]
where [tex]opp=AB[/tex] and [tex]adj=BC[/tex]
Thus, we have;
[tex]tan \ C=\frac{AB}{BC}[/tex]
Substituting the values, we get;
[tex]tan \ C=\frac{7}{25}[/tex]
Thus, the ratio of tan C is [tex]\frac{7}{25}[/tex]
