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anemone
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In triangle $PQR$, $\tan P,\,\tan Q,\,\tan R$ are integers, find their values.
anemone said:In triangle $PQR$, $\tan P,\,\tan Q,\,\tan R$ are integers, find their values.
kaliprasad said:Do not ask me how to derive but ...
In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
To find the value of $\tan P$, we can use the formula $\tan P = \frac{opposite}{adjacent}$, where opposite refers to the length of the side opposite to angle $P$ and adjacent refers to the length of the side adjacent to angle $P$ in the triangle $PQR$.
Yes, it is possible for the tangent of an angle in a triangle to be undefined. This occurs when the adjacent side is equal to 0, making the ratio $\frac{opposite}{adjacent}$ undefined.
If we are only given the angle $Q$ and not the lengths of the sides, we cannot find the exact value of $\tan Q$. However, we can use the general formula $\tan Q = \frac{opposite}{adjacent}$ and assign arbitrary values to the opposite and adjacent sides to find an approximate value of $\tan Q$.
Yes, we can find the value of $\tan R$ in a triangle $PQR$ even if the angle $R$ is not a right angle. We can use the formula $\tan R = \frac{opposite}{adjacent}$, where opposite refers to the length of the side opposite to angle $R$ and adjacent refers to the length of the side adjacent to angle $R$.