List the side lengths of △CDE in order from smallest to largest, given that m∠C=96°, m∠D=44°, and m∠E=40°.
Question
List the side lengths of △CDE in order from smallest to largest, given that m∠C=96°, m∠D=44°, and m∠E=40°.
Solution
In a triangle, the size of an angle is directly proportional to the length of the opposite side. This means that the larger the angle, the longer the side opposite it.
Given that m∠C=96°, m∠D=44°, and m∠E=40°, we can say that:
- The side opposite ∠C (which we'll call side c) is the longest because ∠C is the largest angle.
- The side opposite ∠D (which we'll call side d) is the next longest because ∠D is the next largest angle.
- The side opposite ∠E (which we'll call side e) is the shortest because ∠E is the smallest angle.
So, the side lengths of △CDE in order from smallest to largest are: e, d, c.
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