Answer:
- RS = 2/3·LM
- ST = 2/3·MN
- RT = 2/3·LN
Explanation:
You want the ratios of corresponding side lengths in the similar triangles RST and LMN.
Angles
The missing angles in each triangle can be found from the angle sum theorem, which says the sum of angles in a triangle is 180°.
S = 180° -44° -15° = 121°
N = 180° -121° -44° = 15°
Congruent angle pairs are ...
15°: T, N
44°: R, L
121°: S, M
The congruent angles means these triangles are similar, so we expect side length ratios to be the same for corresponding side lengths.
Side ratios
Corresponding sides are ones that have the same angles on either end. Their ratios are found by dividing the length in triangle RST by the length in triangle LMN.
RS corresponds to LM. RS/LM = 3.61/5.415 = 2/3
ST corresponds to MN. ST/MN = 9.71/14.565 = 2/3
RT corresponds to LN. RT/LN = 11.97/17.955 = 2/3
Then the relationships are ...
- RS = 2/3·LM
- ST = 2/3·MN
- RT = 2/3·LN
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