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

Use the given right triangle to find ratios, inreduced form, for sin A, cos A, and-example-1
User Ziya Mert Karakas
by
3.3k points

1 Answer

22 votes
22 votes

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=(BC)/(AB) \\ \sin A=(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=}(AC)/(AB) \\ \cos \text{ A=}(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=}(BC)/(AC) \\ \tan \text{ A=}(5)/(12) \end{gathered}

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

User Rampal Chaudhary
by
3.6k points
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