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WJEC MATHEMATICS

INTERMEDIATE

ANGLES AND GEOMETRY

TRIGONOMETRY

(SOHCAHTOA)

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Contents

SoHCaHToA

Finding Lengths

Finding Angles

Worded Questions

Credits

WJEC Question bank

http://www.wjec.co.uk/question-bank/question-search.html

PixiMaths

Trigonometry Exercise

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SOHCAHTOA

The triangle above is a right angled triangle with another angle

named theta ( )

The hypotenuse is always the side opposite the right angle

We label the adjacent side the side that touches the angle

(That is not the hypotenuse)

We label the opposite side the side that does not touch the

angle

From a right angled triangle labelled in this way, there are three

trigonometric ratios to learn

Often, the "cover up" method is the simplest to use.

O = opposite A = adjacent H = hypotenuse

S = C = T =

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When answering these questions there are some steps that we do

every time.

Step 1: Label the two sides to use (Either both known or one

known and one to find)

Step 2: Select the triangle needed from the three seen on the

previous page

Step 3: Cover up the letter we need to find to form an equation

Step 4: Substitute values and solve

Finding a missing side

Example 1

Find

Step 4 - Substitute and solve

Step 1

Label the two sides.

The first is the hypotenuse which is

labelled and the second is the unknown

side which is adjacent to the angle

Step 2

We need to select the triangle that

contains a 'h' and an 'a'

Step 3

Cover up the letter of the unknown (a) and

form an equation

x

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Example 2

Find

Step 4 - Substitute and solve

Step 1

Label the two sides.

The first is the side opposite to the angle

(45) and the second is the unknown side

which is adjacent to the angle

Step 2

We need to select the triangle that

contains an 'o' and an 'a'

Step 3

Cover up the letter of the unknown (a) and

form an equation

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Finding a missing angle

The steps to finding a missing angle in a right angled triangle, using

SOHCAHTOA trig, are the same as finding a side length

Example

Find the size of the angle marked

Step 4

Substitute the values and solve

Important! We want on its own!

The inverse of

Step 1

Label the two sides.

The first is the hypotenuse and the second

is the side that is opposite the angle

marked

Step 2

We need to select the triangle that

contains a 'h' and an 'o'

Step 3

Cover up the letter of the unknown and

form an equation

We know the values of 'o' and 'h'

so we cover the 's'

Remember: the 's' stands for

Type this into your calculator!

To get press shift - sin

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Worded / Picture Questions

Very often the question will be 'hidden' within a worded question or

picture.

Angle of elevation

The right angled triangle may be hidden in an angle of elevation

Bearings

Right angled triangles also make an appearance in Bearings

questions

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Exercise G23

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Exam Questions G35

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2.

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3.

4.