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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
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Solution
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.
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