Question

8. A cable car travels 2236 m to climb a mountain that is 1000 m high. It then travels 1414 m to descend 1000 m on the other side of the mountain. A tunnel goes straight through the mountain, from the starting point to the endpoint of the cable car's journey. How long is the tunnel?

Answer 1

Answer:

3000 m

Step-by-step explanation:

Using Pythagoras theorem

$2236^2=1000^2+|AB|^2\\|AB|^2=2236^2-1000^2\\|AB|^2=3999696\\|AB|=\sqrt{3999696} \\=1999.9$

Similarly

$1414^2=1000^2+|BC|^2\\|BC|^2=1414^2-1000^2\\|BC|^2=999696\\|BC|=\sqrt{999696} \\=999.7m$

Length of the Tunnel = |AB|+|BC|

=1999.9+999.7

=2999.6

=3000 m