SOLUTION: Suppose you travel north for 65 kilometers then travel east for 75 kilometers. How far are you from your starting point?
Answer and show your work.
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Question 85948: Suppose you travel north for 65 kilometers then travel east for 75 kilometers. How far are you from your starting point?
Answer and show your work. Found 2 solutions by bucky, chitra:Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Imagine that you are starting at the origin of a coordinate system for graphing. Then imagine
that you go up the y-axis 65 units. At that point you turn 90 degrees to the right and go
horizontally (parallel to the x-axis) 75 units. Stop at that point (75, 65). The distance
from this point to the origin is what you are looking for. Notice that you have formed a
right triangle. From the origin you went 65 units to the right angle. After making the right
angle turn you went 75 units. So the right triangle has 65 and 75 as its legs. The hypotenuse
of the right triangle is the distance from the end of the second leg to the origin.
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You can use the Pythagorean theorem to find the hypotenuse which is the distance you are looking
for. Recall that the Pythagorean theorem says that the sum of the squares of the two legs
of a triangle is equal to the square of the hypotenuse. In equation form this is:
.
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where "a" and "b" are the two legs and "c" is the hypotenuse. In this problem we can
say that a = 65 and b = 75 so the equation becomes:
.
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If you square 65 you get 4225 and if you square 75 you get 5625. Substituting these values
makes the equation become:
.
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adding the two terms on the left side results in:
.
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Finally, to find c you can take the square root of both sides:
.
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This tells you that if you go north 65 km and then east 75 km you will be 99.25 km (rounded
to the nearest hundredth) from the starting point.
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Hope this explanation helps you to see your way through the problem.
You can put this solution on YOUR website! This can be solved using the pythagoras theorem.
The square root of the sum of the squares of these two sides gives us the total distance travelled from the starting point..
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