Question

question
in $\triangle hij$, the measure of $\angle j = 90^\circ$, $ji = 7$, $ih = 25$, and $hj = 24$. what ratio represents the sine of $\angle i$?
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Explanation:

Step1: Recall the definition of sine in a right triangle

In a right triangle, the sine of an acute angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. For $\angle I$ in right triangle $\triangle HIJ$ with $\angle J = 90^{\circ}$, we need to identify the opposite side and the hypotenuse with respect to $\angle I$.

Step2: Identify the sides relative to $\angle I$

• The hypotenuse of a right triangle is the side opposite the right angle. Since $\angle J = 90^{\circ}$, the hypotenuse is $IH$. Given that $IH = 25$.
• The side opposite $\angle I$ is $HJ$. Given that $HJ = 24$.

Step3: Calculate $\sin(\angle I)$

Using the definition of sine, $\sin(\angle I)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{HJ}{IH}$. Substituting the given values, we get $\sin(\angle I)=\frac{24}{25}$.

Answer:

$\frac{24}{25}$