If a right-angled triangle has one side measuring 8cm and another measuring 15cm, what is the length of the hypotenuse?
What is meant by the word hypotenuse?The hypotenuse is the side of a triangle opposite to the right angle. It is the longest of the three sides and can often be identified as the 'diagonal' side of the triangle.
What is pythagorus' theorem?Simply put: a2+ b2=h2 where 'h' is the length of the hypotenuse, 'a' is the length of the second side and 'b' is the length of the third side.
How can we use it to answer this question?In this example, we are trying to work out the length of 'h'.-First, we need to plug the numbers into our equation.-Let's say that 'a' measures 8cm and 'b' measures 15cm.82+ 152=h264 + 225 =h2289 = h2Now we know the length of 'h2' but not h; therefore, the find 'h' we should square root our answer.The square root of 289= 17=> Therefore, h=17 cm.ALWAYS REMEMBER UNITS
A further example: A triangle has a hypotenuse with a length of 8cm and a second side with a length of 6cm. What is the length of the final side?-> First, let's identify the sides in the question.h=8cma=6cmb=?-> Now, let's plug those into our formula: a2+b2=h2-> 62 + b2=82-> 36 + b2=64-> We need to make b2 the subject of our formula, so...to get it by itself, we can subtract 36 from both sides.-> b2= 64 - 36-> b2= 28-> We know what b2 is so we can find it's square root to calculate b.-> The square root of 28=5.49cm (2 dp)
