State whether the following are true or false. Justify your answer.
$ \sec A=\frac{12}{5} $ for some value of angle $ A $.
Given:
Given statement is:
\( \sec A=\frac{12}{5} \) for some value of angle \( A \).
To do:
We have to state whether the given statement is true or false.
Solution:
$\sec\ A =\frac{Hypotenuse}{side\ adjacent\ to\ A}$
$=\frac{AC}{AB}$
In a triangle ABC, $AC$(Hypotenuse) is greater than $AB$.
Therefore,
$\frac{AC}{AB}$ is greater than 1.
This implies \( \sec A=\frac{12}{5} \) for some value of angle \( A \).
The given statement is true.
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