Pythagoras Theorem and Trigonometry Revision Questions Form Two Basic Mathematics

Pythagoras Theorem and Trigonometry Revision Questions Form Two Basic Mathematics

Statistics Revision Questions Form Three Basic Mathematics, Statistics Revision Questions Form Two Basic Mathematics, Pythagoras Theorem and Trigonometry Revision Questions Form Two Basic Mathematics, Geometrical Transformation Revision Questions Form Two Basic Mathematics, Congruence and Similarity Revision Questions Form Two Basic Mathematics, Quadratic Equation Revision Questions Form Two Basic Mathematics, Logarithms Revision Questions Form Two Basic Mathematics, Algebra Revision Questions Form Two Basic Mathematics, Radical Revision Questions Form Two Basic Mathematics, Exponents Revision Questions Form Two Basic Mathematics

Pythagoras Theorem and Trigonometry Revision Questions Form Two Basic Mathematics

A. Pythagoras Theorem

Triangle with a Right angle i.e. 90° has an amazing property. Do you want to know what property is that? Go on, read our notes to see the amazing property of a right angled triangle.

Pythagoras Theorem deals only with problems involving any Triangle having one of its Angles with 900. This kind of a Triangle is called Right angled triangle.

When triangle is a right angled triangle, squares can be made on each of the three sides. See illustration below:

040523 1415 TOPIC8PYTHA1

The Area of the biggest square is exact the same as the sum of the other two squares put together. This is what is called Pythagoras theorem and it is written as:

040523 1415 TOPIC8PYTHA2

that is:

040523 1415 TOPIC8PYTHA3

c’ is the Longest side of the Triangle, is called Hypogenous and is the one that forms the biggest square. a and b are the two smaller sides.

Proof of Pythagoras Theorem

The Pythagoras Theorem

Prove the Pythagoras theorem

Pythagoras theorem states that: In a Right Angled Triangle, the sum of squares of smaller sides is exactly equal to the square of Hypotenuse side (large side). i.e. a2 + b= c2

Take a look on how to show that a2 + b2 = c2

See the figure below:

040523 1415 TOPIC8PYTHA4

The area of a whole square (big square)

A big square is the one with sides a + b each. Its area will be:

(a + b) ×(a + b)

Area of the other pieces

First, area of a smaller square (tilted) = c2

Second, area of the equal triangles each with bases a and height b:

040523 1415 TOPIC8PYTHA5

But there are 4 triangles and they are equal, so total area =

040523 1415 TOPIC8PYTHA6

Both areas must be equal, the area of a big square must be equal to the area of a tilted square plus the area of 4 triangles

That is:

(a + b)(a + b) = c2 + 2ab

Expand (a +b)(a + b): a2 +2ab + b2 = c2 + 2ab

Subtract 2ab from both sides: a2 + b2 = c2 Hence the result!

Note: We can use Pythagoras theorem to solve any problem that can be converted into right Angled Triangle.

Pythagoras Theorem and Trigonometry Revision Questions Form Two Basic Mathematics

KILIMANJARO Form Four Mock Exams May 2025, SIHA DC TERMINAL EXAMINATION DARASA LA TANO 2025, MOEDP Grade Four (Standard Four) Monthly Assessment Exams May 2025

B. Trigonometric Rations

Trigonometry is all about Triangles. In this chapter we are going to deal with Right Angled Triangle. Consider the Right Angled triangle below:

040523 1418 TOPIC9TRIGO1

The sides are given names according to their properties relating to the Angle .

Adjacent side is adjacent (next to) to the Angle

Opposite side is opposite the Angle

Hypotenuse side is the longest side

Sine, Cosine and Tangent of an Angle using a Right Angled Triangle

Define sine, cosine and tangent of an angle using a right angled triangle

Trigonometry is good at finding the missing side or Angle of a right angled triangle. The special functions, sine, cosine and tangent help us. They are simply one of a triangle divide by another. See similar triangles below:

040523 1418 TOPIC9TRIGO2

The ratios of the corresponding sides are:

040523 1418 TOPIC9TRIGO3

Where by tc and s are constant ratios called tangent (t), cosine (c) and sine (s) of Angle respectively.

The right-angled triangle can be used to define trigonometrical ratios as follows:

040523 1418 TOPIC9TRIGO4

The short form of Tangent is tan, that of sine is sin and that of Cosine is cos.

The simple way to remember the definition of sine, cosine and tangent is the word SOHCAHTOA. This means sine is Opposite (O) over Hypotenuse (H); cosine is Adjacent (A) over Hypotenuse (H); and tangent is Opposite (O) over Adjacent (A). Or

040523 1418 TOPIC9TRIGO5

Example 1

Given a triangle below, find sine, cosine and Tangent of an angle indicated.

040523 1418 TOPIC9TRIGO6

Solution

040523 1418 TOPIC9TRIGO7

Pythagoras Theorem and Trigonometry Revision Questions Form Two Basic Mathematics


DOWNLOAD PDF

Leave a Comment

Darasa Huru: JOIN OUR WHATSAPP GROUP

You cannot copy content of this page. Contact Admin