Triangles are those closed convex polygons having three sides. We have already familiar with the different types of triangles. Right angled triangle is the one in which one of the interior angle of a triangle is a right angle. The longest side of the right triangle is called its Hypotenuse and the other two sides including the right angle are called as its legs or the base and the perpendicular. It is very much necessary to learn more about the right angled triangle, as it is very much helpful to find the height of a building, distance between the two buildings, vertical height of an aeroplane at a given instant etc. In this section let us discuss about the different formulae we use for a given right angled triangle.

Area of Right Angle Triangle:

The following diagram shows the right triangle.
RT

The area of a right angled triangle is given by the formula,
Area = $\frac{1}{2}$ x Base x Height
= $\frac{1}{2}$ x leg 1 x leg 2



Right Angle Triangle Equations

If a, b, c are the sides of a right angled triangle such that c > b > a, then the sides of the triangle will satisfy the equation,

c2 = a2 + b2


Solved Examples

Question 1: Find the area of a right angled triangle whose sides including the right angles measure 10 cm and 9 cm respectively.
Solution:
 
From the given data, the legs measure, 10 cm and 9 cm respectively.
Therefore, Area of the right triangle = $\frac{1}{2}$ x 10 x 9

                                                   = $\frac{90}{2}$ = 45 cm2
 

Question 2: Find the length of the hypotenuse of a right triangle whose measures of the other two sides are 8 cm and 6 cm respectively.
Solution:
 
We are given that a = 6 cm and b =  8 cm.
These measures, will satisfy the equation, c2 = a2 + b2
                                                      =>    c2 = 62 + 82 
                                                                  = 36 + 64
                                                                  = 100
                                                                  = 102
                                                     =>      c = 10 cm
 

Question 3: A ladder of 17 m long, reaches the window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.
Right Angled Triangle Example

Solution:
 
From the above figure, the sides of the triangle will satisfy the equation,
                                a2 + b2  = c2
                      =>    152 + b2   = 172 [ substituting, a = 15 and c = 17 ]
                      =>    225 + b2   = 289
                      =>             b2   = 289 - 225
                                             = 64
                                             = 82
                     =>                 b = 8 cm
Therefore, the foot of the ladder from the building is 8 cm.