sally is on a scavenger hunt. a clue tells her to walk 100 steps due south from the starting point and then walk west when she gets to the next clue she will be approximately 150 steps from where she started. how many steps west should she take?

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Ashraf82 Ashraf82 · Answer 1 · 2019-05-04T07:59:21+02:00

Answer:

She should take 112 steps west

Step-by-step explanation:

* Lets explain the relation between the four directions

- North and South on the same line by in opposite directions

- East and West on the same line by in opposite directions

- East and West are perpendicular to the North and South

* Now lets study the situation i the problem

- Sally 100 steps due to South from the starting point

- Then she walk West when she gets the next clue

- The distance between her starting point and ending point is 150 steps

∵ The South is perpendicular to the West

- Lets consider her trip is a right angle triangle ABC, where AB

her steps South and BC her steps West and AC the distance

between her starting point and ending point

∵ AB = 100

∵ AC = 150

∵ m∠B = 90°

- By using Pythagoras theorem

∵ BC = √(AC² - AB²)

∴ BC = √(150² - 100²) = 50√5 = 111.8 steps

* She should take 112 steps west