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GCSE Trigonometry slideshow examples
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โฆ sin-cosec
โฆ cos-sec
โฆ tan-cot
Right Angled Triangle
๐ฝ
๐
๐
๐
Right Angled Triangle
๐ฝ
๐
๐
๐
Trigonometric Ratios of Angles
โ
โ
โ
โ
Measure of green colored side can be found using the Pythagoras
theorem.
เฌถ
เฌถ
= ๐
เฌถ
โ ๐ = ๐ 2
โ
๐
โ
๐๐
โ
Ratios
Sine
Cosine
Tangent
Well Known Trigonometric Ratios
โ ๐๐
โ ๐๐
โ ๐๐
โ ๐
โ Ratios
Sine 0
Cosine 1
Tangent 0
Practice Problems
โ
Find the values of ๐ฅ and ๐ฆ.
sin 32 =
cos 32 =
Note: The calculator settings should be in degrees.
Practice Problems
โ
Find the values of ๐ฅ and โ.
tan 25 =
cos 25 =
Practice Problems
Find the length of ๐ถ๐ท ๐ถ๐ท = 16.5 cm
Practice Problems
โ
๐๐
โ
The height of the isosceles triangle? 2.
Practice Problems
What should be angle ๐, if the area of the triangle is 50
โ
Practice Problems
Work out the value of angle ๐
๐ = 42.
โ
Practice Problems
The Purewal Cruise ship sets off from A, sails West 10 Km then North 20 Km. It ends up at B. What is the
bearing of B from A?
270 + tan
เฌฟ เฌต (2)
I put a ladder 1.5m away from a tree. The ladder is inclined at 70ยฐ above the horizontal. What is the
height of the tree?
Ship B is 100m east of Ship A, and the bearing of Ship B from Ship A is 30ยฐ. How far due North is the
ship?
โ = 4.
Practice Problems
๐ฅ =
1
12
Determine ๐ฅ Determine ๐
๐ = 18.
โ
Practice Problems
Determine ๐
๐ = 67.
โ
1
1
1
1
๐ เฌต
๐ เฌถ
๐ เฌท
1
๐ เฌธ
The angles ๐ เฌต
, ๐ เฌถ
, โฆ form a sequence. Give the formula for the
๐
th term of the sequence.
๐ เฏก
= tan
เฌฟ เฌต
1
n
Practice Problems
A builder places a 2.9 m ladder on horizontal ground, resting against a vertical wall. To be safe to use,
the base of the ladder must be 1.3 m away from the wall. How far up the wall does the ladder reach?
2.6 m
Work out the value of ๐ฅ if the area of the parallelogram is 20 3 square units.
๐ฅ = 5
Practice Problems
An architect wants to calculate the height of a building. He stands 50 m away from the base of the
building and looks up at the top of the building. The angle of elevation from the architect to the top of the
building is 70ยฐ. Calculate the height of the building. Give the answer to one decimal place.
137.4 m
From the top of a 72 m high vertical cliff, a boat has an angle of depression of 32ยฐ. How far is the boat
from the base of the cliff? Give the answer to 1 decimal place.
115.2 m
Bill is 30 m away from the church. The angle of elevation when he looks at the top of the churchโs spire is
45
โ
. If Billโs eye level is 1.5m above the ground, how tall is the church spire?
31.5 m
Practice Problems
Jess looks downwards at a frisbee that has landed 4 m away from her feet. If Jessโ eye level is 1.7 m above
the ground, find the angle of depression.
23
โ
OL and NL are two ladders leaning against a vertical wall NM.
๐๐ = 12
๐ฟ๐ = 6.
โ ๐๐ฟ๐ = 49.
โ
Find the length of the line ๐๐
Find the size of the โ ๐๐ฟ๐
๐๐ = 4.
โ ๐๐ฟ๐ = 12.
โ
3D Trigonometry and Pythagoras
A B
C D
E F
G
H
Diagonal measure ๐ด๐บ
Diagonal measure ๐ด๐น
๐ด๐บ
เฌถ = ๐ด๐ต
เฌถ
เฌถ
๐ด๐น
เฌถ = ๐ด๐บ
เฌถ
เฌถ
3D Trigonometry and Pythagoras
A
B
C
D
V
O
Height ๐๐
Diagonal measure ๐ถ๐
๐๐ถ
เฌถ
=
๐ด๐ต
เฌถ
เฌถ
2
๐๐ถ
เฌถ = ๐๐
เฌถ
เฌถ
๐
tan ๐ =
๐๐
๐๐ถ
