Pythagoras
Pythagoras theorem states that the sum of the squares of the length of 2 legs of a right angled triangle is
equal to the square of the hypotenuse of that triangle.
In more simple terms that means that if, you make a square
that has side lengths equal to that of the hypotenuse, it will
have the same area as the squares made from the lengths of
the other two sides. See example on the left.
In maths terms:
𝑐 2 = 𝑎2 + 𝑏 2
If you want to find the length of any side, you will need to rearrange the equation slightly.
To find the hypotenuse c:
𝑐 = √𝑎2 + 𝑏 2
To find the length of either leg, a or b:
𝑎 = √𝑐 2 − 𝑏 2
𝑏 = √𝑐 2 − 𝑎2
Examples:
c = _____________________
b = _____________________
c = _____________________
b = _____________________
c = _____________________
b = _____________________
c = _____________________
b = _____________________
Trigonometry
Trigonometry is the study of triangles and the relationship between their sides and angles.
The sides of a triangle are given names depending on which angle you are considering, they are called;
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
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Hypotenuse - the longest side
Opposite – the side on the opposite side of the triangle
Adjacent – the side next to the angle
The ratios between the sides of a right-angled triangle are given the names, Sine, Cosine, and Tangent.
If you are given the size of an angle and of one of the sides of the triangle, you can calculate the other
sides by rearranging the above formulas.
Step 1. Identify the names of each side the triangle in relation to the given angle
Step 2. Identify which formula contains the side you know and the unknown side you are trying to
calculate.
Step 3. Write down the formula
Step 4. Substitute the known values.
Step 5. Rearrange to find the unknown.
Example:
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i.
ii.
Calculating the angle
If you are given 2 sides of the triangle the formulas can be rearranged to find an angle in the triangle.
The process is the same as above.
Angle B: _________________________
Angle C: _________________________
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Angle P: _________________________
Angle T: _________________________
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