Lesson: Real-Life Applications of the Pythagorean Theorem

Determine the length of , given that and are two right-angled triangles, , , and .

Ancient Egyptians created right triangles using ropes with 13 equally spaced knots. The first and last knots (knots 1 and 13) were fixed together on the floor to form one vertex of the triangle. At which other two knots could the rope be fixed to form a right angle at knot 1?

A zip line was installed at an outside playground. It is 15.5 m long and attached to two posts 15 m apart on a flat ground. Given that at the arrival post, the zip line must be 1.5 metres above the ground, at what height should it be attached to the other post? Give your answer correct to one decimal place.