If these three segments are connected end-to-end to form a triangle, will the triangle be acute, right, or obtuse?
Correct answer: Obtuse
Let's start by checking if it's a right triangle. If it were right, then the longest side (length 8) would need to be the hypotenuse, and the other two sides (lengths 5 and 6) would need to be the two legs, and which meet at a right angle.
So we can test if the triangle is right by checking if the Pythagorean identity is true given the lengths of the three sticks: does
Therefore, the triangle is not right.
Also, we can see from these calculations that
This means that the triangle will be obtuse because the "extra" length of the longest side stretches the opposite angle to a measure greater than
Older Puzzles of The Week
- how would you know what these angles add up to
- blue x orange = what
- What is the length of the red perimeter
- Geometry Warmup - Angles and Lines
- How many isosceles triangles
- which shape has a greater perimeter
- The quadratic with a root of a root of a quadratic
- is it possible
- a tower of threes
- Playing With Circle's
- Playing with numbers
- can you logic this out
- do we need this many guards
- if Godzilla keeps growing
- this ball is half and half
- What do you know about base angles of isosceles triangles
- two animals are skydiving on the moon
- the solutions to this problem are more beautiful than you'd expect
- color the rest!
- there’s a clever solution...
- this isn’t your average 99 cent store…
- it’ll always bounce back...
- Formula One race cars
- The burning rope
- Socks in the dark
- Lily Pad