Question

1. a ladder 5 m long leans against a wall. its foot is 1.8 m from the base of the wall. how high up the wall does the ladder reach? give your answer to 3 s.f.

hint: draw it out 2 marks

Explanation:

Identify the given values

We have a right triangle formed by the wall, the ground, and the leaning ladder.

• Hypotenuse (ladder length) \(c = 5\text{ m}\)
• Base (distance from wall) \(a = 1.8\text{ m}\)
• Height (reach up the wall) \(b\) is the unknown.

Apply the Pythagorean theorem

Using the Pythagorean Theorem for a right-angled triangle:

$$ a^2 + b^2 = c^2 $$

Substitute the known values:

$$ 1.8^2 + b^2 = 5^2 $$

Solve for the unknown height

Calculate the squares and isolate \(b^2\):

$$ 3.24 + b^2 = 25 $$

$$ b^2 = 25 - 3.24 = 21.76 $$

$$ b = \sqrt{21.76} \approx 4.66476\text{ m} $$

Round to significant figures

Using the Significant Figures knowledge point, we round the result to 3 significant figures:

$$ b \approx 4.66\text{ m} $$

Answer:

\(4.66\text{ m}\)