Head First 2D Geometry

142 Chapter 3

mind the gap

What’s the longest the rope can be without going below the

safety line?

4m + 2m = 6m

So, how far can you swing on a six-meter rope?

Safety line

The floor

4m

2m

The gap between the platforms is the base of a triangle, with the rope

making up two of the sides joined at the point where the rope is fixed at the

top. So the distance of the gap is the same as the length of the base of the

triangle.

2m

This 2m is below the safety line, so

not included

Only add up the

heights ABOVE the

safety line.

We need to find the

distance of this gap.

This angle isn’t

a right angle.

Safety line

The floor

4m

2m

d

you are here 4 143

the pythagorean theorem

Well, the rope doesn’t change

length, does it? So I guess that gives

us two sides of the triangle, but we

can’t use the Pythagorean Theorem

to find the missing side without a

right angle, can we?

How can you make the swing problem into a

right triangle problem so that you can use the

Pythagorean Theorem to find length d?

Safety line

The floor

4m

2m

d

6m

That’s right—the Pythagorean Theorem

only finds missing sides for right

triangles.

So, when you’re faced with a triangle without a right

angle you’ve got two options: find something else in

your Geometry Toolbox to solve the problem, or see if

you can somehow turn your non-right triangle into ...