Question

You are buying materials to build a zip line between your house and a tree that is 45 feet away. You plan to connect the cable to the tree 30 feet above the ground, and to the back of your house 6 feet above the ground. How long is the zip line?

Write this equation with words and symbols (The length of the zip line is the square root of the sum of the squares of the horizontal and vertical distances)

Available words
(Distance from house to tree)
(Height of upper connection)
(Height of lower connection)
(Length of zip line)

Use any mathematical symbols for example
(Radicals, squares [4x4 is 4 squared], +, -, etc)

Answer 1

Solution:

Question: A zip line is to connected between a house and a tree .The upper connection which is the uppermost point of the tree 30 feet tall, from there a cable is to be connected to the back of the house 6 feet above the ground that is height of lower connection.Find the length of Zip line, which is given by     square root of the sum of the squares of the horizontal and vertical distances.

Solution:

That is in symbols, if we use the following notation

Distance from house to tree= D=45 feet

Height of upper connection=30 feet=T

Height of lower connection= 6 feet= L

Joining the upper part of house to tree (Horizontally)

Distance from upper part of house to tree (i.e a horizontal straight line)= 45 feet

Distance where the line cuts the tree and upper part of tree= 30-6=24 feet

Using Pythagorean theorem ,in the right triangle

Length of zip line

= Square root of the sum of the squares of the horizontal and vertical distances                                                                                                        =$\sqrt{24^2+45^2}=\sqrt{576+2045}=\sqrt{2601}=51$ feet