Two ladders, each 5 m long, lean against two different vertical walls…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two ladders, each long, lean against two different vertical walls. Each ladder touches its wall at a height of . The foot of the first ladder is from its wall. Show that the two ladders make congruent triangles with the ground and the wall, and find how far the foot of the second ladder is from its wall.
Need a reminder? The key ideaShow
ASA: two angles and the side between them. AAS: two angles and a side elsewhere; use the angle sum to turn it into ASA. SSS: three sides. RHS: a right angle, the hypotenuse and one side. AAA and SSA are not rules.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The triangles. In each triangle the wall and the ground meet at a right angle. The ladder is the hypotenuse.
Step 2. The equal parts.
- The right angles are equal.
- The hypotenuses are equal: both ladders are long.
- The heights on the walls are equal: both are .
Step 3. The rule. The two triangles are congruent by RHS. By CPCT the distances along the ground are equal.
Step 4. The number. The second foot is also from its wall.
Answer: .
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