walked 5 miles north 7 miles east then 3 miles north to my freimds house how many miles in a straight line?

Question

show work

Answer 1

Well, you have to work this problem as a triangle. One side of the triangle will be 8, since you walked 8 miles in the same general direction. The second side will be 7, since you walked 7 miles in a different direction. You must now find the 3rd side (or hypoteneuse), which will give you the straight distance from beginning to end. The formula for a triangular distance equation (Pythagorean Theorem) is:

a^2 + b^2 = c^2

so, if:
a = 8
b = 7

then:

a^2 = 64
b^2 = 49

and:

a^2 + b^2 = 64 + 49 = 113

so:

c^2 = 113
c = sq. root of 113 (approximately 10.63 miles)


I should just add...that is a hell of a long way to walk just to go to your friend's house. I would take a cab if I were you.

Answer 2

ROUGHLY 10 miles. Take the 5 miles north and add it to the 3 miles north. You get 8. Let the north miles = A and the east miles = B. Use the pythagorean theorem (A squared + B squared = C squared) :

8 ^2 + 7^2 = C^2
64+49=C^2
64+49=103

Rough estimate gives the hypoteneuse (C) the value of 10.


PS...I would use your calculator to deterrmine the sq. root of 103 as necessary for your class.

Answer 3

neglecting the curvature of the earth and the topography in general...

if you draw this out and connect the start and endpoints you will see the interior angles (let's call the value A) are equivalent. Therefore arctan(A) = 3/(7-x) = 5/x and

3x = 35 - 5x

therefore x = 35/8 and 7-x = 21/8

therefore the hypoentuses are
sqrt[ (35/8)^2+5^2] + sqrt[(21/8)^2+ 3^2]
sqrt[(1225+1600)/64] + sqrt[(441+576)/64]
[sqrt(2825)+sqrt(1017)]/8
[5sqrt(113)+3sqrt(113)]/8
sqrt(113)

Answer 4

8

Answer 5

I would like to give Laffy extra points for being the only answer that realized that the TOTAL distance north was important to solving the problem. It is 10.63!

Answer 6

without taking your pen off the paper -
draw a line 5cm long.
then a 7cm line 90degrees left.
then a 3cm line 90degrees right.

then measure the distance between the start and finish point and it should be 11cm = 11 miles walked in a straight line.

Answer 7

8 miles straight.

Answer 8

Use the Pythagorean Theorem

a squared + b squared = c squared.

let a be your total northerly distance and b = your total easterly distance. Then your straight line distance would be c.

Answer 9

15 MILES

Answer 10

10.5 miles. Go figure it out yourself.