# trig problem solving

#### 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. Find:
a) the length of the extended ladder

#### Ackbeet

MHF Hall of Honor
A cute problem. What steps have you taken so far?

#### pickslides

MHF Helper
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?

#### Soroban

MHF Hall of Honor
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.