Answered

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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.

Sagot :

ANSWER

0.5m UP

EXPLANATION

Given:

Determine the value of x at 3m using Pythagorean Theorem

[tex]\begin{gathered} Hyp^2\text{ = Opp + Adj}^2 \\ 6^2\text{ = x}^2\text{ + 3}^2 \\ x^2\text{ = 36 - 9} \\ x\text{ = }\sqrt{27} \\ x\text{ = 5.2} \end{gathered}[/tex]

Determine the value of x at 2m using Pythagorean Theorem

[tex]\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{ = }\sqrt{32} \\ x\text{ = 5.7} \end{gathered}[/tex]

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

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