The distance between points Z and X in the three-dimensional coordinate system is approximately 643.58 inches.
In the given scenario, it appears that a three-dimensional coordinate system is being used, with points represented by (x, y, z) coordinates. To determine the measure of ZX, the distance between points Z and X needs to be calculated using the three-dimensional distance formula:
The distance (D) between two points (x_1, y_1, z_1) and (x_2, y_2, z_2) is given by:
![\[ D = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2) \]](https://img.qammunity.org/2024/formulas/mathematics/college/5afiubcwsk1zlc3fe45igtj6nmeeuexsxt.png)
Applying this formula to the points Z (0, 0, 210) and X (410, 450, 0), the calculation is as follows:
![\[ D = √((410 - 0)^2 + (450 - 0)^2 + (0 - 210)^2) \]](https://img.qammunity.org/2024/formulas/mathematics/college/u6ipvyj809x4s76fpypiajkch9wi4tw9eq.png)
![\[ D = √(410^2 + 450^2 + 210^2) \]](https://img.qammunity.org/2024/formulas/mathematics/college/sc6awabm2y4woszxw419wn0f3piyuvk4m3.png)
![\[ D = √(168100 + 202500 + 44100) \]](https://img.qammunity.org/2024/formulas/mathematics/college/7le5n3a80crdvb07kzwkeour2n1b5n2q72.png)
![\[ D = √(414700) \]](https://img.qammunity.org/2024/formulas/mathematics/college/mtmltn67lnkl9eysvreugy3a4e0ie7d538.png)
![\[ D \approx 643.58 \]](https://img.qammunity.org/2024/formulas/mathematics/college/dfdl9yvcnzhc672rkwq6l509fd6b1t6wxt.png)
Therefore, the measure of ZX is approximately 643.58 inches. If you require this value rounded to the nearest degree, please provide more context, as distance measurements are typically given in inches, and rounding to the nearest degree is more applicable to angles than distances.
Complete question:
In AXYZ, x = 410 inches, y = 450 inches and z=210 inches. Find the measure of ZX to the nearest degree.