Question

In right triangle ABC with right angle at C, find sin A, COS A and tan A, if side a = 8, side b = 15 and side c=17 sin A= cos A=tan A=

Answer 1

A diagram of the right triangle ABC with right angle at C is shown in the following image:

We are going to assume that side a is opposite to angle A, side b is opposite to angle B, and that side c is opposite to angle C:

We are asked to find sinA, cosA, and tanA.

First, let's remember the definitions for sine, cosine, and tangent for any angle X:

`\begin{gathered} \sin X=\frac{opposite\text{ side}}{hypotenuse} \\ \cos X=\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \tan X=\frac{opposite\text{ side}}{adjacent\text{ side}} \end{gathered}`

In this case, for angle A:

The opposite side to angle A is a=8

The adjacent side to angle A is b=15

The hypotenuse is c=17.

Substituting these values to find the sine of A:

`\begin{gathered} \sin A=\frac{opposite\text{ side}}{hypotenuse} \\ \sin A=(8)/(17) \end{gathered}`

We do something similar to find the cosine of A:

`\begin{gathered} \cos A=\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \cos A=(15)/(17) \end{gathered}`

And finally, the tangent of A is:

`\begin{gathered} \tan A=\frac{opposite\text{ side}}{adjacent\text{ side}} \\ \tan A=(8)/(15) \end{gathered}`

Answer:

`\begin{gathered} \sin A=(8)/(17) \\ \cos A=(15)/(17) \\ \tan A=(8)/(15) \end{gathered}`