Question

State whether the following is true or false.
sec A = $\frac{12}{5}$ for some value of angle A.

• A. True
• B. False

Answer 1

The correct option is A True

Let a $\Delta$ABC in which $\angle B={90}^{\circ }$, AC be 12k and AB be 5k, where k is a positive real number.
By pythagoras theorem we get,
$A{C}^2=A{B}^2+B{C}^2$
$(12k{)}^2=(5k{)}^2+B{C}^2$
$B{C}^2+25k^2=144k^2$
$B{C}^2=119k^2$
Such a triangle is possible as it will follow the pythagoras theorem.