What is the hypotenuse ?

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

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.

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 .

Which trigonometric ratio is often used 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 (the 'opposite' side) and the horizontal distance from an object (the 'adjacent' side).

For which angle (between 0º and 90º) is the tangent of it undefined ?

The tangent of the angle 90º is undefined .

GCSEMathsAQAHigherFlashcards4. Geometry & MeasuresPythagoras & Trigonometry

Pythagoras & Trigonometry (AQA GCSE Maths)

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FrontPythagoras Theorem
What is the hypotenuse?
FrontPythagoras Theorem
State the equation, in terms of $a$ , $b$ , and $c$ , for Pythagoras' theorem, where $c$ is the length of the hypotenuse.
BackPythagoras Theorem
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

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Cards in this collection (28)

What is the hypotenuse?
The hypotenuse is the longest side in a right-angled triangle.
It is located opposite the right angle.
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?
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.
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 in a right-angled triangle?
To find the length of one of the shorter sides in a right-angled triangle, use the equation $a = \sqrt{c^{2} - b^{2}}$ or $b = \sqrt{c^{2} - a^{2}}$ .
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 SOHCAHTOA equation for sine.
The SOHCAHTOA equation for sine is $\sin (θ) = \frac{Opposite}{Hypotenuse}$ .
State the SOHCAHTOA equation for cosine.
The SOHCAHTOA equation for cosine is $\cos (θ) = \frac{Adjacent}{Hypotenuse}$ .
State the SOHCAHTOA equation for tangent.
The SOHCAHTOA equation for tangent 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 side 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 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 (the 'opposite' side) and the horizontal distance from an object (the 'adjacent' side).
What is the exact value of the cosine of 0º?
The exact value of the cosine of 0º is 1.
$\cos (0) = 1$ .
What is the exact value of the sine of 90º?
The exact value of the sine of 90º is 1.
$\sin (90) = 1$ .
What is the exact value of the tangent of 0º?
The exact value of the tangent of 0º is 0.
$\tan (0) = 0$ .
What is the exact value of the tangent of 45º?
The exact value of the tangent of 45º is 1.
$\tan (45) = 1$ .
What is the exact value of both the cosine and the sine of 45º?
The exact value of both the cosine and the sine of 45º is $\frac{\sqrt{2}}{2}$ .
This can also be written as $\frac{1}{\sqrt{2}}$ .
$\cos (45) = \sin (45) = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$ .
The sine of which angle (between 0º and 90º) has an exact value of $\frac{1}{2}$ ?
The sine of 30º has an exact value of $\frac{1}{2}$ .
$\sin (30) = \frac{1}{2}$ .
What is the exact value of the cosine of 90º?
The exact value of the cosine of 90º is 0.
$\cos (90) = 0$ .
The tangent of which angle (between 0º and 90º) has an exact value of $\frac{\sqrt{3}}{3}$ ?
The tangent of 30º has an exact value of $\frac{\sqrt{3}}{3}$ .
$\tan (30) = \frac{\sqrt{3}}{3}$ .
What is the exact value of the tangent of 60º?
The exact value of the tangent of 60º is $\sqrt{3}$ .
$\tan (60) = \sqrt{3}$ .
What is the exact value of the cosine of 60º?
The exact value of the cosine of 60º is $\frac{1}{2}$ .
$\cos (60) = \frac{1}{2}$ .
What is the exact value of the sine of 0º?
The exact value of the sine of 0º is 0.
$\sin (0) = 0$ .
For which angle (between 0º and 90º) is the tangent of it undefined?
The tangent of the angle 90º is undefined.
What is the exact value of both the cosine of 30º and the sine of 60º?
The exact value of both the cosine of 30º and the sine of 60º is $\frac{\sqrt{3}}{2}$ .
$\cos (30) = \sin (60) = \frac{\sqrt{3}}{2}$ .

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