An Introduction to Trigonometry
Required Knowledge: An understanding of similarity and congruence.
Ability to work with ratios
1. Bring up Page 2 on the smart board. Talk about how you can change the shape by using the 8 handles on the picture. Make copies of the picture.
· When are they similar?
· When are they congruent?
· When is one an enlargement of another?
2. Use the photographs on pages 3 &4 on the smartboard to explain what they will need to measure for the versions they are about to be given. (length,width, diagonal, angle)
3. Hand out Pages 3 and 4 (as one A3 sheet) and page 7 to each pair. They will also need a protractor and a ruler. In pairs, they should complete the table on Page 7, looking for any patterns they do so.
4. Class Discussion on the activity and anything they noticed. In particular
· What relationships are there between C and E ?
(Congruent rectangles: This example may be helpful to refer back to when you need to explain why we need to label the sides opp, adj and hyp.)
· What relationships are there between C and F
(Similar rectangles: They should notice the ratios are the same which should remind them of previous work done where they noticed that the ratios were the same when the “angle” was the same)
· How could you find the length of the diagonal without measuring it?
(A link to Pythagoras)
5. In pairs or small groups use their completed tables to answer the worksheet questions on Pages 5 & 6. You could optionally get the students to complete the table on Page 8 to help them with this.
Follow up: Re-labelling of sides
Students could plot the ratios given on autograph and then the trig graphs could be added to show the relationship of the ratio with the angle. The graph could then be used to estimate the answers to further angle problems before finally introducing cos, sin, tan and the calculator buttons
An Introduction to Trigonometry
An Introduction to Trigonometry
Worksheet
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1.
2..
3.
4. You are given a poster of your favourite pop star. It is 75cm wide and 56.25 cm high. What angle will the diagonal make with the bottom of the poster?
5. Artists and architects use the golden ratio in their work as this ratio produces art that is most aesthetically pleasing. This ratio is (approximately) 1.62 An artist wishes to construct a canvas where the ratio of height to width is 1.62. If he wants the diagonal to be 50cm, what will the width and height need to be?
6. The guy rope of a tent makes an angle of 58° with the ground. The guy rope is 1.5m long. How high from the ground is the rope attached to the tent?
7. A sunshade is to be hung outside a shop . The slope on the sunshade is to be 35° to the horizontal and the sunshadw must extend 3m from the shopfront. What length of material is required for the sunshade?
8. A 3.5m fishing rod is resting at the edge of a lake at angle of 41° to the ground.
(a) How high is the tip of the rod above the ground?
(b) What distance does the rod reach across the lake?
9. The latest man made ski slope covers 30m of land and is 42.4m high.at the top. Assuming the slope is constant, what angle does the slope make with the ground?
Page 3
An Introduction to Trigonometry
Complete this table of results for each photograph you have been given.
Photograph / Height / Width / Diagonal / Angle / Width ¸ Diagonal / Height ¸ Diagonal / Height ¸ WidthA
B
C
D
E
F
An Introduction to Trigonometry
Use this table to help you complete the worksheet
Question / Height / Width / Diagonal / Angle / Width ¸ Diagonal / Height ¸ Diagonal / Height ¸ Width1
2
3
4
5
6
7
8
9
Page 3