Question

. Solve the following problem using analytical techniques: Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position?

Answer 1

To find the distance from the starting point to the final position, use the Pythagorean theorem. To find the compass direction, use trigonometry.

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem and trigonometry. Let's start by finding the distance from the starting point to the final position.

Using the Pythagorean theorem, we can calculate the length of the diagonal (R) formed by the two sides, which are the distances walked west (A) and north (B).

R = sqrt(A^2 + B^2) = sqrt((18.0)^2 + (25.0)^2) = 30.0 m (rounded to one decimal place).

To find the compass direction of the line connecting the starting point to the final position, we can use trigonometry. We can calculate the angle (theta) using the inverse tangent function:

theta = arctan(B / A) = arctan(25.0 / 18.0) = 53.1 degrees (rounded to one decimal place) north of west.

Answer 2

H = 30.8 m

`\theta =54.25^0`

Step-by-step explanation:

given,

first walks straight west = 18 m

then straight in north = 25 m

the distance from the start point

H² = B² + P²

H² = 18² + 25²

`H = √(18^2+25^2)`

`H = √(324+625)`

H = 30.8 m

the angle between

`tan \theta = (P)/(B)`

`tan \theta = (25)/(18)`

`\theta = tan^(-1)((25)/(18))`

`\theta =54.25^0`