Answer:
y = 6√3
Step-by-step explanation:
The Pythagorean theorem applies.
... TM² + NT² = NM²
... 6² + y² = (9+3)²
... y² = 12² -6² = 108
... y = √108
... y = 6√3
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You may recognize this as a 30°-60°-90° triangle, which has sides in the ratio ...
... 1 : √3 : 2
For triangle MTN, the scale factor on this ratio is 6: the sides have ratios ...
... 6 : 6√3 : 12