Question

determine the distance a player travels from (0, 0, 0) to (28, 15, 10).
a. 34.52
b. 30.24
c. 33.30
d. 28.93
which of these scenarios would not typically require the use of the pythagorean theorem in three - dimensions?
a. finding the diagonal length of a box
b. calculating the length of a ramp
c. determining the straight - line distance between two points
d. measuring the circumference of a circle

Explanation:

Step1: Recall 3 - D distance formula

The distance $d$ between two points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ in three - dimensions is given by $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}$. Here, $(x_1,y_1,z_1)=(0,0,0)$ and $(x_2,y_2,z_2)=(28,15,10)$.

Step2: Substitute values into formula

$d=\sqrt{(28 - 0)^2+(15 - 0)^2+(10 - 0)^2}=\sqrt{28^2+15^2+10^2}=\sqrt{784 + 225+100}=\sqrt{1109}\approx33.30$.

For the second question:

Step1: Analyze each option

• Option a: Finding the diagonal length of a box in 3 - D uses the three - dimensional Pythagorean theorem $d=\sqrt{l^{2}+w^{2}+h^{2}}$.
• Option b: Calculating the length of a ramp (in a 3 - D context) can use the Pythagorean theorem if considering horizontal, vertical and slant distances.
• Option c: Determining the straight - line distance between two points in 3 - D can use the 3 - D distance formula which is based on the Pythagorean theorem.
• Option d: Measuring the circumference of a circle uses the formula $C = 2\pi r$ and has nothing to do with the Pythagorean theorem in three - dimensions.

Answer:

First question: c. 33.30
Second question: d. Measuring the circumference of a circle