Define the term hypotenuse .

The hypotenuse is the longest side in a right-angled triangle . It is located opposite the right angle.

What does Pythagoras' theorem state?

Pythagoras' theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides .

True or False? Pythagoras' theorem applies to equilateral triangles.

False. Pythagoras' theorem can only be used on right-angled triangles . An equilateral triangle contains no right-angles, however, an isosceles or scalene triangle may also be a right-angled triangle.

Define the term trigonometry .

Trigonometry is the mathematics of angles in triangles . It looks at the relationship between side lengths and angles of triangles.

What does SOHCAHTOA stand for?

SOHCAHTOA is a mnemonic to help you remember the different trigonometric ratios.It stands for Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.

What type of triangles can SOHCAHTOA be used on?

SOHCAHTOA can only be used on right-angled triangles .

What labels are given to the sides of a triangle when using SOHCAHTOA?

The three sides are labelled the Hypotenuse (the length opposite the right-angle), the Adjacent (the side next to the angle in question) and the Opposite (the side opposite the angle in question).

What is the angle of elevation ?

The angle of elevation is the angle between the horizontal and the line of sight when looking up at an object.

What is the angle of depression ?

The angle of depression is the angle between the horizontal and the line of sight when looking down at an object.

Which trigonometric ratio is often used for in problems involving angles of elevation and depression?

The trigonometric ratio that is often used in real-life scenarios with angles of elevation and depression is the tangent ratio . This is because real-life questions are often concerned with the height of an object or the horizontal distance from an object.

IGCSEMaths A: HigherEdexcelFlashcards

Right-Angled Triangles - Pythagoras & Trigonometry (Edexcel IGCSE Maths A)

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Cards in this collection (17)

Define the term hypotenuse.
The hypotenuse is the longest side in a right-angled triangle. It is located opposite the right angle.
What does Pythagoras' theorem state?
Pythagoras' theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
True or False?
Pythagoras' theorem applies to equilateral triangles.
False.
Pythagoras' theorem can only be used on right-angled triangles.
An equilateral triangle contains no right-angles, however, an isosceles or scalene triangle may also be a right-angled triangle.
State the equation, in terms of $a$ , $b$ , and $c$ , for Pythagoras' theorem where $c$ is the length of the hypotenuse.
The equation for Pythagoras' theorem is $a^{2} + b^{2} = c^{2}$
Where:
- $a$ and $b$ are the lengths of the two shorter sides
- $c$ is the length of the hypotenuse
True or False?
To find the length of the hypotenuse, you add inside the square root.
True.
To find the length of the hypotenuse, you add inside the square root using $c = \sqrt{a^{2} + b^{2}}$
What is the equation to find the length of one of the shorter sides?
To find the length of one of the shorter sides, use the equation $a = \sqrt{c^{2} - b^{2}}$ or $b = \sqrt{c^{2} - a^{2}}$ .
Define the term trigonometry.
Trigonometry is the mathematics of angles in triangles. It looks at the relationship between side lengths and angles of triangles.
What does SOHCAHTOA stand for?
SOHCAHTOA is a mnemonic to help you remember the different trigonometric ratios.It stands for Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
State the equation for the sine function.
The equation for the sine function is $\sin (θ) = \frac{Opposite}{Hypotenuse}$ .
State the equation for the cosine function.
The equation for the cosine function is $\cos (θ) = \frac{Adjacent}{Hypotenuse}$ .
State the equation for the tangent function.
The equation for the tangent function is $\tan (θ) = \frac{Opposite}{Adjacent}$ .
What type of triangles can SOHCAHTOA be used on?
SOHCAHTOA can only be used on right-angled triangles.
What does the inverse trigonometric function do, e.g. $\sin^{- 1}$ ?
The inverse trigonometric function is used to find missing angles when two sides of a right-angled triangle are known, e.g. $θ = \sin^{- 1} (\frac{Opposite}{Hypotenuse})$ .
What labels are given to the sides of a triangle when using SOHCAHTOA?
The three sides are labelled the Hypotenuse (the length opposite the right-angle), the Adjacent (the side next to the angle in question) and the Opposite (the side opposite the angle in question).
What is the angle of elevation?
The angle of elevation is the angle between the horizontal and the line of sight when looking up at an object.
What is the angle of depression?
The angle of depression is the angle between the horizontal and the line of sight when looking down at an object.
Which trigonometric ratio is often used for in problems involving angles of elevation and depression?
The trigonometric ratio that is often used in real-life scenarios with angles of elevation and depression is the tangent ratio. This is because real-life questions are often concerned with the height of an object or the horizontal distance from an object.

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2. Equations, Formulae & Identities

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4. Geometry & Trigonometry

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