Question

A ladder is 6 m long. How much farther up a wall does the ladder reach when the base of the ladder is 2 m from the wall than when it is 3 m from the wall? Round to the nearest tenth of a meter.

Answer 1

0.5m UP

Step-by-step explanation

Given:

Determine the value of x at 3m using Pythagorean Theorem

`\begin{gathered} Hyp^2\text{ = Opp + Adj}^2 \\ 6^2\text{ = x}^2\text{ + 3}^2 \\ x^2\text{ = 36 - 9} \\ x\text{ = }√(27) \\ x\text{ = 5.2} \end{gathered}`

Determine the value of x at 2m using Pythagorean Theorem

`\begin{gathered} Hyp^2\text{ = Opp}^2\text{ + Adj}^2 \\ 6^2\text{ = x}^2\text{ + 2}^2 \\ x^2\text{ = 36 -4} \\ x\text{ = }√(32) \\ x\text{ = 5.7} \end{gathered}`

The Difference

5.7 - 5.2 = 0.5 m

Hence, the ladder reach 0.5m farther up when the base of the ladder is 2 m from the wall than when it is 3 m from the wall