Question

State whether the following are true or false. Justify your answer.

sec A = `12/5` for some value of angle A.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

sec A = `12/5`

`"Hypotenuse"/"Side adjacent to ∠A" -  12/5`

`("AC")/("AB") = (12/5)`

Let AC be 12k, AB will be 5k, where k is a positive integer.

Applying Pythagoras theorem in ΔABC, we obtain

AC² = AB² + BC²

(12k)² = (5k)² + BC²

144k² = 25k² + BC²

BC² = 119k²

BC = 10.9k

It can be observed that for given two sides AC = 12k and AB = 5k,

BC should be such that,

AC − AB < BC < AC + AB

12k − 5k < BC < 12k + 5k

7k < BC < 17 k

However, BC = 10.9k

Clearly, such a triangle is possible and hence, such value of sec A is possible.    

Hence, the given statement is true.