Question

The treasure map said to start at the old oak tree, walk 70 paces north, then 40 paces East, then dig. What is the straight-line distance (in paces) from the tree to the treasure?

Answer 1

Answer:

The straight-line distance (in paces) from the tree to the treasure is 80.62 paces

Step-by-step explanation:

Given:

Distance walked towards the north = 70 Paces

Distance walked towards the East = 40 Paces

To Find:

The straight line distance  from the tree to the treasure =?

Solution:

We we track the trail we can find a right triangle formed where the two sides are 70 pace and 40 pace each. The straight line distance is the hypotenuse of the triangle(Refer the figure below

Now we can find the length of the hypotenuse by Pythagorean theorem

$a^2 =b^2 +c^2$

where b and c are the sides of the triangle

and a is the hypotenuse

$a^2 = 70^2 +40^2$

$a^2 =4900 + 1600$

$a = \sqrt{4900 + 1600}$

$a =\sqrt{6500}$

a =  80.62