Final answer:
The relationship between point z and the triangle is determined using the Pythagorean theorem. The length of GZ is approximately 17.35 units when GU is 18 units and ZT is 4.8 units. Calculations for OT require additional information from the provided figures.
Step-by-step explanation:
To determine the relationship between point z and the triangle, as well as the lengths of GZ and OT, it is important to utilize the Pythagorean theorem and trigonometry. The Pythagorean theorem is a fundamental principle in geometry that relates the three sides of a right triangle. The theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be expressed as: a² + b² = c², where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. If GU is the hypotenuse and its length is 18 units, and ZT is one of the sides with a length of 4.8 units, we can calculate the length of GZ using the theorem:
- From the Pythagorean theorem, GZ² = GU² - ZT².
- GZ² = 18² - 4.8² = 324 - 23.04 = 300.96.
- GZ = √300.96 which is approximately 17.35 units.
For the second part of the question regarding the length of OT, if we know the length of ZT is 4.8 units, we must identify the right triangle in which OT is a side. Without a specific figure reference, it is impossible to provide the correct calculations for the length of OT.