find hj. write your answer as an integer or as a decimal rounded to the nearest tenth. hj =
find hj. write your answer as an integer or as a decimal rounded to the nearest tenth. hj =
Answer
Explanation:
Step1: Identify the trig - ratio
In right - triangle $\triangle HIJ$, we know the length of the hypotenuse $HI=\sqrt{97}$ and we want to find the side $HJ$. Since $\cos I=\frac{IJ}{HI}$ and $\sin I = \frac{HJ}{HI}$, and $\angle I = 69^{\circ}$, we use the sine function.
Step2: Apply the sine formula
The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin I=\frac{HJ}{HI}$, so $HJ = HI\times\sin I$. We know that $HI = \sqrt{97}\approx9.85$ and $\sin69^{\circ}\approx0.934$. So $HJ=\sqrt{97}\times\sin69^{\circ}\approx9.85\times0.934 = 9.2$.
Answer:
$9.2$