Question

The sine, cosine, and tangent ratios each have a reciprocal ratio. The reciprocal ratios are cosecant (csc), secant (sec), and cotangent(cot). Use AABC and the definitions below to write the ratio sec A.

Answer 1

Given the triangle with the following sides

`\begin{gathered} BC=45 \\ AB=51 \\ AC=24 \end{gathered}`

We can find the value of Sec A below.

Step-by-step explanation

From trigonometry

`SecA=(1)/(CosA)`

Also

`\begin{gathered} CosA=\frac{Adjacent\text{ }side}{Hypotenuse\text{ Side}}=(AC)/(AB)=(24)/(51) \\ \\ \end{gathered}`

Therefore;

`\begin{gathered} SecA=1/(24)/(51) \\ SecA=1*(51)/(24) \\ SecA=(51)/(24) \\ SecA=(17)/(8) \end{gathered}`

Answer

`(17)/(8)`