Question

Use the given right triangle to find ratios, inreduced form, for sin A, cos A, and tan A.

Answer 1

In the given right triangle,

BC=5

AC=12.

Hypotenuse of the triangle, AB=13.

Now, the ratio of sin A can be expressed as,

$\sin A=\frac{opposite\text{ side}}{hypotenuse}$

The opposite side to angle A is BC.

Hence,

$\begin{gathered} \sin A=\frac{BC}{AB} \\ \sin A=\frac{5}{13} \end{gathered}$

The ratio of cos A can be expresssed as,

$\cos \text{ A=}\frac{\text{adjacent side}}{hypotenuse}$

The side adjacent to angle A is AC.

Hence,

$\begin{gathered} \cos \text{ A=}\frac{AC}{AB} \\ \cos \text{ A=}\frac{12}{13} \end{gathered}$

The ratio tan A can be expressed as,

$\begin{gathered} \tan \text{ A=}\frac{\text{opposite side}}{adjacent\text{ side}} \\ \tan \text{ A=}\frac{BC}{AC} \\ \tan \text{ A=}\frac{5}{12} \end{gathered}$

Therefore, sin A=5/13, cos A=12/13 and tan A=5/12.