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. 943
c. 1024
d. 965

Explanation:

Step1: Find differences in coordinates

Let \((x_1,y_1,z_1)=(300,500,0)\) and \((x_2,y_2,z_2)=(600,900,800)\).
\(\Delta x=x_2 - x_1=600 - 300 = 300\), \(\Delta y=y_2 - y_1=900 - 500 = 400\), \(\Delta z=z_2 - z_1=800 - 0 = 800\).

Step2: Apply distance formula in 3D

The distance formula in 3 - D is \(d=\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}\).
Substitute \(\Delta x = 300\), \(\Delta y = 400\), \(\Delta z = 800\) into the formula:
\(d=\sqrt{300^{2}+400^{2}+800^{2}}=\sqrt{90000 + 160000+640000}=\sqrt{890000}\approx943\).

Answer:

B. 943