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.

True or False? Using the other acute angle in the same triangle swaps the opposite and adjacent sides.

True. The opposite and adjacent are named relative to the angle you choose, so they exchange roles. The hypotenuse is unaffected, because it is fixed by the right angle rather than by your choice of angle.

How do you decide which trigonometric ratio to use to find a missing length?

Label the sides, then choose the ratio that uses the side you know and the side you want. Substitute the values, keeping brackets around the angle, then rearrange to make the unknown length the subject.

When finding an angle, how do you choose which trigonometric ratio to use?

Look at which two sides you have been given, then pick the ratio built from those two. Here both lengths are known and the angle is the unknown, which is the reverse of the situation when you are finding a length.

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 .

GCSEMathsEdexcelFoundationFlashcardsGeometry & MeasuresPythagoras & Trigonometry

Pythagoras & Trigonometry (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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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 (33)

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 $b = \sqrt{c^{2} - a^{2}}$ .
In a right-angled triangle, how do you label the three sides for trigonometry?
Label them relative to the angle you are using, often marked $θ$ .
The opposite is the side across from that angle, the adjacent is the side next to it, and the remaining side is the hypotenuse.
What does SOHCAHTOA stand for?
It packs the three ratios into one word: $sin θ = \frac{O}{H}$ , $cos θ = \frac{A}{H}$ and $tan θ = \frac{O}{A}$ .
Each group of three letters gives one ratio, with the first letter naming the function and the other two naming the fraction.
True or False?
Using the other acute angle in the same triangle swaps the opposite and adjacent sides.
True.
The opposite and adjacent are named relative to the angle you choose, so they exchange roles.
The hypotenuse is unaffected, because it is fixed by the right angle rather than by your choice of angle.
How do you decide which trigonometric ratio to use to find a missing length?
Label the sides, then choose the ratio that uses the side you know and the side you want.
Substitute the values, keeping brackets around the angle, then rearrange to make the unknown length the subject.
A right-angled triangle has an angle of 43°, with the opposite side $x$ and the adjacent side 9 cm. Complete the working:
$tan (43) = \frac{x}{9}$ , so $x = 9 \times______=______$ cm
The completed working is:
$x = 9 \times tan (43) = 8.39$ cm
The unknown sits on top of the fraction, so multiplying both sides by 9 releases it, and the answer is given to 3 significant figures.
True or False?
These trigonometric ratios work in any triangle.
False.
The ratios $sin$ , $cos$ and $tan$ apply only to right-angled triangles.
Without a right angle there is no hypotenuse for the other two sides to be measured against.
When finding an angle, how do you choose which trigonometric ratio to use?
Look at which two sides you have been given, then pick the ratio built from those two.
Here both lengths are known and the angle is the unknown, which is the reverse of the situation when you are finding a length.
How do you get from $cos y = \frac{8}{23}$ to the angle $y$ ?
Apply the inverse cosine, written ${cos}^{- 1}$ .
So $y = {cos}^{- 1} (\frac{8}{23})$ , which gives 69.6° to 1 decimal place.
Where do you find the inverse trigonometric functions on a calculator?
Above the $sin$ , $cos$ and $tan$ keys, reached using the shift key.
They are labelled ${sin}^{- 1}$ , ${cos}^{- 1}$ and ${tan}^{- 1}$ .
Complete the two rounding conventions by filling in the missing numbers:
A missing length is given to $______$ significant figures unless you are told otherwise.
A missing angle is given to $______$ decimal place unless you are told otherwise.
The completed conventions are:
A missing length is given to 3 significant figures unless you are told otherwise.
A missing angle is given to 1 decimal place unless you are told otherwise.
True or False?
You can find an angle using $tan$ if you know the hypotenuse and the opposite side.
False.
$tan$ is built from the opposite and the adjacent, so those are the two sides it needs.
Given the opposite and the hypotenuse you would use $sin$ instead.
A right-angled triangle has an opposite side of 5 cm and an adjacent side of 12 cm. Which calculation gives the angle?
Take the inverse tangent of $\frac{5}{12}$ , because the opposite and the adjacent are the two sides you have.
That is ${tan}^{- 1} (\frac{5}{12})$ , giving an angle of 22.6° to 1 decimal place.
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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