find the sine of $angle u$.\nsimplify your answer and write it as a proper fraction, improper fraction, or…
find the sine of $angle u$.\nsimplify your answer and write it as a proper fraction, improper fraction, or whole number.\n$sin(u) = $
Answer
Explanation:
Step1: Identify congruent triangles
Triangles $\triangle QRS$ and $\triangle UTV$ are congruent (right triangles with matching side lengths, so $\angle U \cong \angle Q$).
Step2: Recall sine definition for right triangles
For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$.
Step3: Assign sides for $\angle Q$
In $\triangle QRS$, opposite side to $\angle Q$ is $SR = 21$, hypotenuse is $QS = 29$.
Step4: Calculate $\sin(U)$
Since $\angle U = \angle Q$, $\sin(U) = \sin(Q) = \frac{21}{29}$.
Answer:
$\frac{21}{29}$