Thread: trig problem solving

When an extension ladder rests against a wall it reaches 4 m up the wall. The ladder is extended a further 0.8 m without moving the foot of the ladder and it now rests against the 1 m further up. Find:
a) the length of the extended ladder

please show alll working out.

A cute problem. What steps have you taken so far?

Not sure if i'm reading this correctly but if the ladder is extended 0.8m, how can it be 1m further up the wall?

Hello, Tessarina!

When an extension ladder rests against a wall it reaches 4 m up the wall.
The ladder is extended a further 0.8 m without moving the foot of the ladder
and it now rests against the 1 m further up.

a) Find the length of the extended ladder.

The original length of the ladder is L meters.
The foot of the ladder is x meters from the wall.
The ladder reaches 4 meters up the wall.

Code:

      *
      |\ 
      | \
    4 |  \ L 
      |   \
      |    \ 
      * - - * 
         x

We have: .x² + 4² = L² . → . x² = L² - 16 .[1]



When the ladder is extended to a length of L + 0.8 meters,
. . it reaches 5 meters up the wall.

Code:

      *
      |\ 
      | \
    5 |  \ L + 0.8
      |   \
      |    \ 
      * - - * 
         x

We have: .x² + 5² = (L + 0.8)² . → .x² = (L + 0.8)² - 25 .[2]



Equate [2] and [1]: .(L + 0.8)² - 25 = L² - 16

. . (L + 0.8)² - L² = 25 - 16 . → . 1.6L = 8.36

. . L = 8.36 ÷ 1.6 . → . L = 5.225


The length of the extended ladder is: .5.225 + 0.8 = 6.025 meters.