Lecture2: Solutions and Application of Right Triangle (Pythagorean Theorem)

SOLUTIONS AND APPLICATIONS OF RIGHT TRIANGLE

RIGHT TRIANGLE – is a triangle with exactly one (1) right angle.

Parts of a Right Triangle

1.       Hypotenuse – is the side opposite the 90^o angle

and it is also considered to be the longest side.

2.       Legs–these are the remaining sides of a

right triangle which may be shorter or longer.

3.       Angles

Pythagorean Theorem

In a right triangle, the square of the hypotenuse is equal to the sum of the square of its legs.
In symbols:

c2 = a2 + b2             or         a2 = c2– b2               or         b2 = c2 – a2

e.g.

1)      a = 8; b = 15; c = ?

c² = a² + b²

c² = 8² + 15²

c² = 64+225

c = sqrt 289

c = 17

2)      a = ?; b = 4; c = 5

a² = c²– b²

a² = 5²– 4²

a² =25– 16

a = sqrt 9

a = 3

3)      a = 12; b = ?; c = 37

b² = c² – a²

b² = 37² – 12²

b² = 1369 –144

b = sqrt 1225

b = 35

Sample Problems

      1)      A wall 12ft high cast a shadow 5ft long from the foot. Find the distance from the top of the wall to the tip of the shadow.

Illustration:

Given: a = 5ft; b = 12ft; c = ?

Solution:c² = a² + b²

                c² = (5ft)² + (12ft)²

               c² = 25ft² + 144ft²

              c = sqrt 169

              c = 13ft

2)      A ladder 9m long is placed 6m from the foot of a tree. Up to what height does the ladder reach the tree?

Illustration:

Given: a = 6m; b =?; c = 9m

Solution:b² = c²– b²

                b² = (9m)² – (6m)²

            b² = 81m² –36m²

            b = sqrt 45

b =  6.71m