List the side lengths of △IJK in order from smallest to largest, given that m∠J=97°, m∠K=37°, and m∠I=46°.

Question

List the side lengths of $\triangle IJK$ in order from smallest to largest, given that $m\angle J=97^\circ$ , $m\angle K=37^\circ$ , and $m\angle I=46^\circ$ .

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Solution

In a triangle, the size of an angle is directly proportional to the length of the side opposite it. This means that the larger the angle, the longer the side opposite it.

Given that m∠J=97°, m∠K=37°, and m∠I=46°, we can see that ∠K is the smallest angle, ∠I is the next largest, and ∠J is the largest.

Therefore, the side opposite ∠K (which is side IJ) is the shortest, the side opposite ∠I (which is side JK) is the next longest, and the side opposite ∠J (which is side KI) is the longest.

So, the side lengths of △IJK in order from smallest to largest are IJ, JK, KI.

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List the side lengths of △IJK in order from smallest to largest, given that m∠J=97°, m∠K=37°, and m∠I=46°.

Question

List the side lengths of △IJK \triangle IJK △IJK in order from smallest to largest, given that m∠J=97∘ m\angle J=97^\circ m∠J=97∘, m∠K=37∘ m\angle K=37^\circ m∠K=37∘, and m∠I=46∘ m\angle I=46^\circ m∠I=46∘.

Solution

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List the side lengths of $\triangle IJK$ in order from smallest to largest, given that $m\angle J=97^\circ$ , $m\angle K=37^\circ$ , and $m\angle I=46^\circ$ .