Find the exact value of $\sin \left( \arctan \frac { 7 } { 24 } \right)$ .
A) $\frac { 24 } { 7 }$
B) $\frac { 7 } { 24 }$
C) $\frac { 7 } { 32 }$
D) $\frac { 7 } { 25 }$
E) $\frac { 32 } { 25 }$

Question

Quizplus · Accepted Answer

To find the exact value of $\sin \left( \arctan \frac { 7 } { 24 } \right)$, consider a right triangle where the opposite side is 7 and the adjacent side is 24. The hypotenuse can be found using the Pythagorean theorem: $\sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25$. Therefore, $\sin$ of the angle is the opposite side over the hypotenuse, which is $\frac{7}{25}$.

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Find the Exact Value Of $\sin \left( \arctan \frac { 7 } { 24 } \right)$