Question

What’s the ratios of each

Answer 1

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

$sin \ C=\frac{opp}{hyp}$

where $opp=AB$ and $hyp=AC$

Thus, we get;

$sin \ C=\frac{AB}{AC}$

Substituting the values, we get;

$sin \ C=\frac{7}{25}$

Thus, the ratio of sin C is $\frac{7}{25}$

Ratio of cos C:

The ratio of cos C can be determined using the trigonometric ratio.

Thus, we have;

$cos C=\frac{adj}{hyp}$

where $adj=BC$ and $hyp=AC$

$cos \ C=\frac{BC}{AC}$

Substituting the values, we get;

$cos \ C=\frac{24}{25}$

Thus, the ratio of cos C is $\frac{24}{25}$

Ratio of tan C:

The ratio of tan C can be determined using the trigonometric ratio.

Thus, we have;

$tan \ C=\frac{opp}{adj}$

where $opp=AB$ and $adj=BC$

Thus, we have;

$tan \ C=\frac{AB}{BC}$

Substituting the values, we get;

$tan \ C=\frac{7}{25}$

Thus, the ratio of tan C is $\frac{7}{25}$