The longest side of a right- angled triangle is called the hypotenuse, which is always opposite the right-angle.
In any right- angled triangle,the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other sides.
For any right-angled triangle, this rule can be used to calculate the length of the hypotenuse if the lengths of the smaller sides are known.
(Hypotenuse)2 = (Shortest side)2 + (Other side)2
(Longest side)2 = (Shortest side)2 + (Other side) 2
(Hypotenuse)2 = (Shortest side) 2 + (Other side) 2
Find the length of the hypotenuse:
Find the length of the missing side:
If (Hypotenuse)2 = (Shortest side) 2 + (Other side)2
Then the triangle is right angled.
Is this a right angled triangle ?
Very often, you will need to solve a question where the use of Pythagoras' Theorem does not seem obvious.
Calculate the perimeter of triangle ABD. (Give your answer correct to 1 dp.)
Finding the perimeter requires the length of CD to be known.
Since ACB is a right angled triangle, Pythagoras' Theorem can be used to find length BC. Triangle BCD is also right angled, so Pythagoras' Theorem can be used again , with the value calculated for BC and the given 11 cm to find CD.
Finally, the lengths can be added to find the perimeter.
Perimeter = 12 + 11 +9 +7.6 = 39.6 cm(1 dp)
The gable of a symmetrical building is painted yellow.
Calculate the area of the painted surface.
This is a composite area, so split into two parts:
A1 is a rectangle,
A2 is a triangle,
To find the perpendicular height, x
Use Pythagoras' Theorem
Substituting into the equation for A2 :
Thus the area of the painted surface
A1 + A2 = 50 + 16.6 = 66.6 m2
Calculate the length of the line that joins the points
A(-5, 10) and B ( 3 ,0 )
Plot the points and draw the line.
Complete the right angled triangle
solve using Pythagoras' Theorem
This is the basis for the distance formula , which is part of Higher Mathematics Applications.