Discovering the Summit of a Mountain Adventure

How can we determine the position of the summit relative to the base camp on a map?

What components need to be considered when measuring the distance between the summit and the base camp?

Calculating the Position of the Summit and Base Camp

When determining the position of the summit relative to the base camp on a map, we need to consider both the horizontal distance and the direction from the camp.

To find the exact location, we can break down the displacement into its north and west components using trigonometry calculations.

Imagine embarking on an exciting mountain adventure and reaching the summit, located 2480 meters above the base camp. The summit, measured on a map to be 4340 meters horizontally from the camp in a direction 38.3° west of north, presents a thrilling exploration challenge.

To determine the position of the summit relative to the base camp, we start by calculating the westward and northward components of the displacement. The westward component is found by multiplying the horizontal distance by the cosine of the angle 38.3° west of north.

Westward component:
4340 m × cos(38.3°) = 4340 m × 0.793 ≈ 3442.62 m

Similarly, the northward component is determined by multiplying the horizontal distance by the sine of the angle:

Northward component:
4340 m × sin(38.3°) = 4340 m × 0.608 ≈ 2641.12 m

Therefore, the summit of the mountain is approximately 3442.62 meters west and 2641.12 meters north of the base camp on the map. This detailed calculation allows you to visualize the exact position of the summit in relation to the adventurous starting point.