Question

1. a hikers current position is at (300m, 500m, 0m) and the peak is at (600m, 900m, 800m). calculate the hiking distance.

a. 1123
b. 1024
c. 943
d. 965

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 3 - D space is given by $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}$. Here, $(x_1,y_1,z_1)=(300,500,0)$ and $(x_2,y_2,z_2)=(600,900,800)$.

Step2: Calculate differences

$x_2 - x_1=600 - 300 = 300$, $y_2 - y_1=900 - 500 = 400$, $z_2 - z_1=800 - 0 = 800$.

Step3: Square the differences

$(x_2 - x_1)^2=300^2 = 90000$, $(y_2 - y_1)^2=400^2 = 160000$, $(z_2 - z_1)^2=800^2 = 640000$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2=90000 + 160000+640000=890000$.

Step5: Take the square - root

$d=\sqrt{890000}\approx943.4$.

Answer:

c. 943