IB Math Studies SL Pythagoras Theorem

Questions and Answers

1. IB Mathematical Studies SL – Pythagoras’ rule

How can I find the length of the hypotenuse in a right angle triangle with known sides 3 cm and 5 cm?

Solution

IB Mathematical Studies SL – Pythagoras’ rule

The rule of Pythagoras states that in a right-angled triangle, with hypotenuse c and the other sides a and b, holds

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

So, in this case, we have that

$c^2=a^2+b^2\Leftrightarrow c^2=3^2+5^2=9+25=34\Leftrightarrow c=\sqrt{34} \ cm$

2. IB Maths Studies Converse of Pythagoras

IB Mathematical Studies SL – Converse of Pythagoras’ rule

How can I check if a triangle with sides 3 cm, 5cm and 8cm is right angled?

Solution

IB Mathematical Studies SL – Converse of Pythagoras’ rule

The Converse Pythagoras’ rule states that if a triangle has sides of length a,b and c where $c^2=a^2+b^2$

then the triangle is right angled.

Therefore, in this case, we have that

Given that in a right-angled triangle the longest side is the hypotenuse

$c^2=8^2=64\not=3^2+5^2=34$

Therefore the triangle is not right-angled.