a hiker walks 14.7 km at an angle of 35 degrees South of East find the East and North components of this walk
East 14.7 cos 35
North -14.7 sin 35
draw it !
To find the East and North components of the hiker's walk, we need to use trigonometry.
Step 1: Determine the East component
To find the East component, we need to find the horizontal distance traveled by the hiker.
Horizontal distance = 14.7 km * cos(35 degrees)
Step 2: Determine the North component
To find the North component, we need to find the vertical distance traveled by the hiker.
Vertical distance = 14.7 km * sin(35 degrees)
Using these formulas, we can calculate the East and North components of the walk.
East component = 14.7 km * cos(35 degrees)
North component = 14.7 km * sin(35 degrees)
To find the East and North components of the hiker's walk, we can use trigonometry. We'll break down the 14.7 km distance into its eastward and northward components using the given angle.
First, let's find the eastward component. We can use the cosine function, which relates the adjacent side to the hypotenuse of a right triangle:
cos(angle) = Adjacent / Hypotenuse
In this case, the angle is 35 degrees, and the hypotenuse is the total distance walked, 14.7 km. Let's calculate:
cos(35) = East / 14.7
Now, solve for East:
East = cos(35) * 14.7
Next, let's find the northward component. We can use the sine function, which relates the opposite side to the hypotenuse of a right triangle:
sin(angle) = Opposite / Hypotenuse
Again, the angle is 35 degrees, and the hypotenuse is 14.7 km. Let's calculate:
sin(35) = North / 14.7
Now, solve for North:
North = sin(35) * 14.7
Now we have the values for East and North components of this walk.