Question

In triangle ijk, measure of angle j =34, measure of angle i=72, and i=206. identify j rounded to the nearest tenth. Please help

Answer 1

We can solve this problem by using the law of sines.

The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

Using this law on our problem, we have the following relation

$\frac{j}{\sin J}=\frac{i}{\sin I}$

We know the measure of 3 of those values. Plugging those values on this equation, we have

$\begin{gathered} \frac{j}{\sin 34^{\circ}}=\frac{206}{\sin 72^{\circ}} \\ j=\frac{206}{\sin72^{\circ}}\cdot\sin 34^{\circ} \\ j=121.121864097\ldots \\ j\approx121.1 \end{gathered}$

The length of j is 121.1.