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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.

The Sine Cosine And Tangent Ratios Each Have A Reciprocal Ratio The Reciprocal Ratios Are Cosecant Csc Secant Sec And Cotangentcot Use AABC And The Definitions class=

Answer :

Given the triangle with the following sides

[tex]\begin{gathered} BC=45 \\ AB=51 \\ AC=24 \end{gathered}[/tex]

We can find the value of Sec A below.

Explanation

From trigonometry

[tex]SecA=\frac{1}{CosA}[/tex]

Also

[tex]\begin{gathered} CosA=\frac{Adjacent\text{ }side}{Hypotenuse\text{ Side}}=\frac{AC}{AB}=\frac{24}{51} \\ \\ \end{gathered}[/tex]

Therefore;

[tex]\begin{gathered} SecA=1\div\frac{24}{51} \\ SecA=1\times\frac{51}{24} \\ SecA=\frac{51}{24} \\ SecA=\frac{17}{8} \end{gathered}[/tex]

Answer

[tex]\frac{17}{8}[/tex]

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