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Raj travelled from a point X straight to Y at a distance of 80 kilometres. He turned right and walked 50 metres, then again turned right and walked 70 metres. Finally, he turned right and walked 50 metres. How far is he from the starting point?
- a)10 metres
- b)20 metres
- c)50 metres
- d)70 metres
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Raj travelled from a point X straight to Y at a distance of 80 kilomet...
To find out how far Raj is from the starting point, we need to analyze his movements step by step.
1. Moving straight from X to Y:
We are given that Raj traveled straight from point X to Y, which is a distance of 80 kilometers. This initial movement does not affect his position in relation to the starting point, as he is moving in a straight line.
2. Turning right and walking 50 meters:
After reaching point Y, Raj turns right and walks 50 meters. This movement creates a right-angled triangle with the starting point as one vertex and the 80-kilometer line as the hypotenuse. The 50-meter line is the adjacent side of this triangle.
3. Turning right and walking 70 meters:
Next, Raj turns right again and walks 70 meters. This creates another right-angled triangle, with the 50-meter line as the hypotenuse. The 70-meter line is the adjacent side of this triangle.
4. Turning right and walking 50 meters:
Finally, Raj turns right once more and walks 50 meters. This creates yet another right-angled triangle, with the 70-meter line as the hypotenuse. The 50-meter line is the adjacent side of this triangle.
Calculating the distance from the starting point:
To find the distance from the starting point, we need to determine the length of the line connecting the starting point to the endpoint of the 50-meter line. This line is the opposite side of the last right-angled triangle formed.
Using Pythagoras' theorem, we can calculate the length of this line:
Opposite side^2 = Hypotenuse^2 - Adjacent side^2
Opposite side^2 = 70^2 - 50^2
Opposite side^2 = 4900 - 2500
Opposite side^2 = 2400
Opposite side = √2400
Opposite side ≈ 48.9898
Therefore, Raj is approximately 49 meters away from the starting point.
Since the closest option to 49 meters is 10 meters, the correct answer is option A) 10 meters.
1. Moving straight from X to Y:
We are given that Raj traveled straight from point X to Y, which is a distance of 80 kilometers. This initial movement does not affect his position in relation to the starting point, as he is moving in a straight line.
2. Turning right and walking 50 meters:
After reaching point Y, Raj turns right and walks 50 meters. This movement creates a right-angled triangle with the starting point as one vertex and the 80-kilometer line as the hypotenuse. The 50-meter line is the adjacent side of this triangle.
3. Turning right and walking 70 meters:
Next, Raj turns right again and walks 70 meters. This creates another right-angled triangle, with the 50-meter line as the hypotenuse. The 70-meter line is the adjacent side of this triangle.
4. Turning right and walking 50 meters:
Finally, Raj turns right once more and walks 50 meters. This creates yet another right-angled triangle, with the 70-meter line as the hypotenuse. The 50-meter line is the adjacent side of this triangle.
Calculating the distance from the starting point:
To find the distance from the starting point, we need to determine the length of the line connecting the starting point to the endpoint of the 50-meter line. This line is the opposite side of the last right-angled triangle formed.
Using Pythagoras' theorem, we can calculate the length of this line:
Opposite side^2 = Hypotenuse^2 - Adjacent side^2
Opposite side^2 = 70^2 - 50^2
Opposite side^2 = 4900 - 2500
Opposite side^2 = 2400
Opposite side = √2400
Opposite side ≈ 48.9898
Therefore, Raj is approximately 49 meters away from the starting point.
Since the closest option to 49 meters is 10 meters, the correct answer is option A) 10 meters.
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Community Answer
Raj travelled from a point X straight to Y at a distance of 80 kilomet...
The movements of Raj are as shown in Figure. (X to Y, Y to A, A to B, B to C). Rajâ's distance from the starting point X = XC = (XY - YC) = (XY - BA) = (80 - 70) m = 10 m.
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Raj travelled from a point X straight to Y at a distance of 80 kilometres. He turned right and walked 50 metres, then again turned right and walked 70 metres. Finally, he turned right and walked 50 metres. How far is he from the starting point?a)10 metresb)20 metresc)50 metresd)70 metresCorrect answer is option 'A'. Can you explain this answer?
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