Question about a word problem?

Question

Suppose you travel north for 65 kilometers then travel east 75 kilometers. How far are you from your starting point?

Answer 1

Pythagoras Theorem
sqrt(65^2+75^2)
= sqrt(9850)
= 99.25km (approx)

Answer 2

It is a right angled triangle and we should use Pythagoras theorem. The distance from the starting point is

sqrt (65 x 65 + 75 x 75) = 99.25 km approx.

Please understand that this is as 'crow flies' i.e. straight line. In real life, it may not be possible to travel like that and you may need to come back by the same way that you went, which will add up to 65 + 75 = 140 kms.

Answer 3

The Pythagoran Theorem says the sum of the squares of the two sides of a triangle equals the square of the hypoteneuse. So 65^2 + 75^2 = X^2

Solving for X gives you an answer of approximately 99.247166 kilometers.

Answer 4

Draw the path you descibe, then draw a straight line between the start and the finish. You'll wind up with a right triangle, with the two "legs" 65 and 75 km respectively, and your answer is the length of the hypothenuse (the longest side).

Use the Pythagorean Theorem (also called "distance formula"):

d = square_root ( a^2 + b^2)

with a=65 and b=75.

Answer 5

Start at point A and travel north 65 kilometers to point B.
From point B, travel east 75 kilometers to point C.

If you travel from point C to point A, then the journey completes a right triangle.

Given the measures of any two sides of a right triangle, we can find the measure of the third side.

Pythagorean theorem: The sum of the squares of the legs equal the square of the hypotenuse.

In this problem's right triangle, segment AB is a leg, segment BC is a leg, and segment CA is the hypotenuse.

(AB)^2 + (BC)^2 = (CA)^2
65^2 + 75^2 = (CA)^2
4225 + 5625 = (CA)^2
9850 = (CA)^2
sqrt(9850) = CA
99.2 = CA

Answer: You are approximately 99.2 kilometers from your starting point (the length of segment CA).

Answer 6

this is a right triangle
solve for the hypotenuse
distance = sqr( 65^2 + 75^2 ) = 99.25 kilometers

Answer 7

Assuming this is not a trick question (for example, where you are close to the north pole or the south pole), then you can work this out by Pythagoras.
d^2 = 65^2 + 75^2.

Answer 8

Using Pythagores theorem...

sqrt( 75^2 + 65^2 )

= 99.247166206396039345852328631456

Answer 9

First remember that The distance 'd' between two points A = (x1, y1) and B = (x2, y2) is given by the formula:

d = sqrt( (x2-x1)^2 + (y2-y1)^2 ), where sqrt means squared root

Your problems can be solved as a coordinated problem where A=(0,0) and B=(75,65), then the distance is:

d = sqrt( (75-0)^2 + (65-0)^2 ) = sqrt ((75^2) + (65^2)) = 99.247166

Answer 10

distance = sqr( 65^2 + 75^2 ) = 99.25 kilometers