Ranjeet parks his car in a lot on the corner of Parklane and Main Street. He walks 100 m east to
first avenue, turns 30% to the left, and follows First avenue for 80 m to the metro building, where
he takes the elevator to his office on the gth 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 the given measurements on the
diagram. (5 marks)e
b) How far is Ranjeet from his car, in a direct line? (6 marks)
a) Here is a diagram representing the given problem:
```
100m
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| Parklane Main |
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30% left | x 80m |
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\ /
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-------------------
```
b) To determine the distance Ranjeet is from his car in a direct line, we can use the Pythagorean theorem. Let's start by finding the length of the horizontal component (x) using the given measurements:
From the diagram, we can see that Ranjeet walks 100 m east to the first avenue, and then turns 30% to the left. Since we don't know the length of the road in this direction, we can calculate it as follows:
Total distance traveled in this direction = (30/100) * 100 m = 30 m.
So, the horizontal component (x) is 30 m.
Next, we need to find the vertical component (y). From the diagram, we can see that Ranjeet walks along the First avenue for 80 m, and each floor in the building is 4 m in height. Therefore, the vertical component (y) can be calculated as:
Total distance traveled in this direction = number of floors * height of each floor = g * 4 m.
Finally, we can use the Pythagorean theorem to find the direct distance (d) from Ranjeet to his car:
d^2 = x^2 + y^2
d^2 = 30^2 + (g*4)^2
d = √(30^2 + (g*4)^2)
Since the value of "g" (number of floors) is not given, we cannot determine the exact value of d without this information.
a) To answer this question, we need to sketch a diagram representing the situation described. Let's start by drawing a simple map:
```
-------------------
| |
| |
| G | <--- Ranjeet's office (gth floor)
| |
| |
---------------------
|First Avenue| |
80m
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| E |
| | |
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| | |
| | |
---------------------
Main Street 100m Parklane
| | 30% turn
| V
|
Ranjeet's
starting
point
```
I have labeled the given measurements on the diagram. The capital "G" represents Ranjeet's office on the gth floor, and the starting point of Ranjeet's walk is marked as well.
b) To determine how far Ranjeet is from his car in a direct line, we can use the Pythagorean Theorem.
First, let's calculate the horizontal distance Ranjeet walked. He walked 100m horizontally before making the 30% left turn. This means he walked 100m * 0.7 = 70m along First Avenue.
Next, we find the vertical distance Ranjeet traveled. Each floor in the building is 4m in height, and he is on the gth floor. Therefore, the vertical distance he traveled is g floors * 4m/floor = 4g meters.
Using these values, we can apply the Pythagorean Theorem to find the direct distance from his office to the car:
Direct distance = sqrt((horizontal distance)^2 + (vertical distance)^2)
= sqrt((70m)^2 + (4g)^2)
The specific value of distance will depend on the floor Ranjeet's office is located on. You can substitute the actual value of g into the equation to calculate the distance.
I made a sketch assuming you meant " turns 30° to the left"
so we can find the distance from the car to the metro building using
the cosine law
x^2 = 100^2 + 80^2 - 2(100)(80)cos 150°
= ..
x = 173.943...
At this point you want to go to the gth floor???
Assuming that was supposed to be an actual number, we can find the
height within the building.
e.g. suppose he goes to the 8th floor, the height would be 32 m
and we can find the distance to the car, call it d
d^2 = 32^2 + x^2 , (x from above)
and d = ....