Question

A helicopter, which starts directly above you, lands at a point that is 4.50 km from your present location and in a direction that is 25° north of east. You want to meet the helicopter at it's landing site, however, you must travel along streets that are oriented either east-west or north-south. What is the minimum distance you must travel to reach the helicopter?

Answer 1

To find the minimum distance to the helicopter, calculate the eastward and northward components using trigonometry and sum them.

Step-by-step explanation:

The minimum distance you must travel to reach the helicopter is determined by decomposing the direct diagonal path into two perpendicular paths that correspond to the grid of streets running east-west and north-south. Since the direction to the helicopter is 25° north of east, you can use trigonometry to find the lengths of the east and north legs of your journey. Using the cosine function for the eastward distance (cos(25°) × 4.50 km) and the sine function for the northward distance (sin(25°) × 4.50 km), you can calculate the exact distances you need to travel east and north:

Eastward distance = cos(25°) × 4.50 km

Northward distance = sin(25°) × 4.50 km

Sum these two distances to get the total minimum distance you need to travel.

Answer 2

5.98 km

Step-by-step explanation:

This question can be easily solved by using the trigonometric properties of a right angled triangle.

See attachment for pictorial explanation

To get x we have

Sinθ = opp / hyp

Sin25 = x / 4.5

x = 4.5 sin 25

x = 4.5 * 0.423

x = 1.9 km

To get y, we have

Cosθ = adj / hyp

Cos25 = y / 4.5

y = 4.5 cos 25

y = 4.5 * 0.906

y = 4.08 km

x + y = 1.9 + 4.09 = 5.98 km

Thus, the minimum distance required is 5.98 km