Question

o. ranjeet parks his car in a lot on the corner of park lane and main street. he walks 80 m east to first avenue, turns 300 to the left, and follows first avenue for 100 m to the metro building, where he takes the elevator to his office on the 15th floor. each floor in the building is 4 m in height. from his office window, ranjeet can see his car in the lot. a) sketch a diagram to represent this problem, labelling all given measurements on the diagram. b) how far is ranjeet from his car, in a direct line?

Answer 1

Using the Pythagorean theorem, Ranjeet is approximately 141.42 meters from his car in a direct line when viewing from his office window on the 15th floor.

Step-by-step explanation:

To determine how far Ranjeet is from his car in a direct line, we will employ the Pythagorean theorem. Since each floor in the building is 4 m in height, Ranjeet is 60 meters (15 floors × 4 meters per floor) above the ground.

The walking path to the building represents two sides of a right-angled triangle, with 80 m being the eastward displacement and 100 m being the northward displacement after the 300 turn. From his office window, the direct line of sight to his car is the hypotenuse of this right-angled triangle formed by the walking path and the vertical distance due to the building's height.

We can calculate the direct line distance (d) using the Pythagorean theorem:
d^2 = horizontal distance^2 + vertical distance^2
d^2 = (80^2 + 100^2) + 60^2
d^2 = 6400 + 10000 + 3600
d^2 = 20000
d = √20000
d ≈ 141.42 m.

Ranjeet is therefore approximately 141.42 meters from his car when looking down from his office window.