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Asha works on a right triangle in which angle A has opposite side 9 cm, adjacent side 12 cm and…

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Asha works on a right triangle in which angle $A$ has opposite side $9\ \text{cm}$ , adjacent side $12\ \text{cm}$ and hypotenuse $15\ \text{cm}$ . She writes:

$\sin A = \dfrac{12}{15}$ , $\quad \tan A = \dfrac{12}{9}$ , $\quad \sec A = \dfrac{15}{9}$ .

Find each mistake and write the correct values.

Need a reminder? The key ideaShow

$\sin A = \dfrac{\text{opp}}{\text{hyp}}$ , $\cos A = \dfrac{\text{adj}}{\text{hyp}}$ , $\tan A = \dfrac{\text{opp}}{\text{adj}}$ . Their reciprocals are $\operatorname{cosec} A$ , $\sec A$ and $\cot A$ . Also $\tan A = \dfrac{\sin A}{\cos A}$ . A ratio depends only on the angle.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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