#### Question

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

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

#### Solution

sec A = 12/5

Hypotenuse/Side adjacent to ∠A - 12/5

AC/AB = 12/5

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

Applying Pythagoras theorem in ΔABC, we obtain

AC^{2} = AB^{2} + BC^{2}

(12*k*)^{2} = (5*k*)^{2} + BC^{2}

144*k*^{2} = 25*k*^{2} + BC^{2}

BC^{2} = 119*k*^{2}

BC = 10.9*k*

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

BC should be such that,

AC − AB < BC < AC + AB

12*k* − 5*k* < BC < 12*k* + 5*k*

7*k *< BC < 17 *k*

However, BC = 10.9*k*. Clearly, such a triangle is possible and hence, such value of sec A is possible.

Hence, the given statement is true.

Is there an error in this question or solution?

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State whether the following are true or false. Justify your answer. sec A = 12/5 for some value of angle A. Concept: Trigonometric Ratios.

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