Question In Delta HIJ,h=97cm,mangle H=144^circ and mangle I=24^circ Find the length of i, to the nearest 10th of a centimeter. Answer Attemptiout of 2 i=square cm

## Step 1: Finding Angle J<br />### The sum of angles in a triangle is 180°. We are given $m\angle H = 144^{\circ}$ and $m\angle I = 24^{\circ}$. Therefore, $m\angle J = 180^{\circ} - 144^{\circ} - 24^{\circ} = 12^{\circ}$.<br /><br />## Step 2: Applying the Law of Sines<br />### The Law of Sines states that $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$. In our case, we have $\frac{h}{\sin H} = \frac{i}{\sin I}$. We are given $h=97$ cm, $m\angle H = 144^{\circ}$, and $m\angle I = 24^{\circ}$. We want to find $i$. So, we have $\frac{97}{\sin 144^{\circ}} = \frac{i}{\sin 24^{\circ}}$.<br /><br />## Step 3: Solving for i<br />### We can solve for $i$ by multiplying both sides of the equation by $\sin 24^{\circ}$: $i = \frac{97 \times \sin 24^{\circ}}{\sin 144^{\circ}}$. Calculating this gives $i \approx \frac{97 \times 0.4067}{0.5878} \approx 67.01$. Rounding to the nearest tenth gives $i \approx 67.0$ cm.