Question

A chair lift at a ski resort travels along the
cable as shown.
0
2
4
14
16
18
6 8 10 12
1 unit = 10 ft
How long is the cable? Round your answer to
the nearest whole foot.

Answer 1

Answer:

$187\ ft$

Step-by-step explanation:

Let

$A(0,3), B(6,5),C(12,4),D(18,2)$

we know that

The length of the cable L is

$L=AB+BC+CD$

The formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

we have

$A(0,3), B(6,5)$

substitute in the formula

$d=\sqrt{(5-3)^{2}+(6-0)^{2}}$

$d=\sqrt{(2)^{2}+(6)^{2}}$

$dAB=\sqrt{40}\ units$

step 2

Find the distance BC

we have

$B(6,5),C(12,4)$

substitute in the formula

$d=\sqrt{(4-5)^{2}+(12-6)^{2}}$

$d=\sqrt{(-1)^{2}+(6)^{2}}$

$dBC=\sqrt{37}\ units$

step 3

Find the distance CD

we have

$C(12,4),D(18,2)$

substitute in the formula

$d=\sqrt{(2-4)^{2}+(18-12)^{2}}$

$d=\sqrt{(-2)^{2}+(6)^{2}}$

$dCD=\sqrt{40}\ units$

step 4

Convert units to feet

we have

1 unit = 10 ft

$dAB=\sqrt{40}\ units=6.32*10=63.2\ ft$

$dBC=\sqrt{37}\ units=6.08*10=60.8\ ft$

$dCD=\sqrt{40}\ units=6.32*10=63.2\ ft$  

step 5

Find the length of the cable

$L=63.2+60.8+63.2=187.2\ ft$

Round to  the nearest whole foot

$187.2=187\ ft$