Question

A jeep travels 29 miles at a bearing of N62°W.
How far north did the jeep travel?

Answer 1

To calculate how far north the jeep traveled with a bearing of N62°W, trigonometry is used. The northward distance is found to be approximately 13.62 miles after computing the cosine of 62° and multiplying by the total travel distance of 29 miles.

Step-by-step explanation:

To determine how far north the jeep traveled with a bearing of N62°W, we can use trigonometry. The northward travel corresponds to the 'opposite' side in a right-angled triangle, while the hypotenuse is the total travel distance (29 miles in this case). We use the cosine function because it relates the adjacent side (northward distance) to the hypotenuse in a right-angled triangle.

Let's consider the following steps:

1. Set up the equation using cosine: cos(62°) = northward distance / 29 miles.
2. Rearrange the equation to solve for the northward distance: northward distance = 29 miles * cos(62°).
3. Compute the value: northward distance ≈ 29 miles * 0.4695 (cosine of 62°)
4. Calculate the approximate distance: northward distance ≈ 13.62 miles.

Therefore, the jeep traveled approximately 13.62 miles to the north.