Final answer:
To find the missing side length of what is assumed to be a right-angled triangle, use the Pythagorean theorem with the given side lengths of 3.7 mm and 7.5 mm. The calculation yields a missing side (hypotenuse) of approximately 8.4 mm to the nearest tenth of a millimeter. If not a right-angled triangle, additional information would be required.
Step-by-step explanation:
The student is asking for help with finding the missing side length of a triangle given two side lengths, 3.7 mm and 7.5 mm, and the answer must be to the nearest tenth of a millimeter. Assuming this is a right-angled triangle and we're using the Pythagorean theorem, which is a2 + b2 = c2, where c is the hypotenuse (the longest side of a right triangle), and a and b are the other two sides.
To find the third side, designate one of the known lengths as 'a' and the other as 'b', then solve for 'c'. For example, if 3.7 mm is a and 7.5 mm is b, then:
- a2 = 3.72 = 13.69
- b2 = 7.52 = 56.25
- c2 = a2 + b2 = 13.69 + 56.25 = 69.94
- c = √69.94
- c ≈ 8.4 mm (to the nearest tenth of a millimeter)
If the triangle is not right-angled, we need more information or a different formula, such as the law of cosines, to find the missing side.