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

`(j)/(\sin J)=(i)/(\sin I)`

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

`\begin{gathered} (j)/(\sin 34^(\circ))=(206)/(\sin 72^(\circ)) \\ j=(206)/(\sin72^(\circ))\cdot\sin 34^(\circ) \\ j=121.121864097\ldots \\ j\approx121.1 \end{gathered}`

The length of j is 121.1.