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1
WJEC MATHEMATICS
INTERMEDIATE
ANGLES AND GEOMETRY
TRIGONOMETRY
(SOHCAHTOA)
2
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
3
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 =
4
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
5
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
6
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
7
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
8
Exercise G23
9
Exam Questions G35
1.
2.
10
3.
4.