a child desires to reach a point that is 3.4km from its present location and in a direction that is 35° north of east.however, it must travel along streets that go either north-south or east-west.
what is the minimum distance he could travel to reach his destination?
use 3.4 km as the hypotenuse of a triangle with a 35º angle
the sum of the other two sides is the minimum distance
X = 3.4*cos35 = 2.79 km.
Y = 3.4*sin35 = 1.95 km.
d = 2.79 + 1.95 =
To find the minimum distance the child needs to travel to reach the destination, we can break down the distance into its north and east components.
Given:
Distance = 3.4 km
Direction = 35° north of east
Step 1: Convert the direction to north and east components
To find the north component, we use the sine of the given angle:
North component = Distance * sin(35°)
North component = 3.4 km * sin(35°)
To find the east component, we use the cosine of the given angle:
East component = Distance * cos(35°)
East component = 3.4 km * cos(35°)
Step 2: Calculate the total distance traveled in each direction
Since the child travels along streets that go either north-south or east-west, the actual distance traveled is the sum of the north component and the east component.
Total distance traveled = North component + East component
Step 3: Calculate the minimum distance traveled
The minimum distance traveled is the straight-line distance from the child's starting point to the destination. This can be calculated using the Pythagorean theorem:
Minimum distance = sqrt((North component)^2 + (East component)^2)
Putting it all together:
1. Calculate the north component: North component = 3.4 km * sin(35°)
2. Calculate the east component: East component = 3.4 km * cos(35°)
3. Calculate the total distance traveled: Total distance traveled = North component + East component
4. Calculate the minimum distance traveled: Minimum distance = sqrt((North component)^2 + (East component)^2)
By following these steps, you can determine the minimum distance the child could travel to reach their destination.