EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Trigonometry 1
Angles and trigonometry · Lesson 6 of 7
Last Lesson and Before
Answer each one, then check.
1. Last lesson: how far apart are (0, 0) and (6, 8)?
10
2. Solve x/4 = 3.
x = 12
3. Solve 12/x = 3.
x = 4
4. Round 6.8829 to 3 significant figures.
6.88
Learning Objectives
1. Label the hypotenuse, opposite and adjacent sides from a given angle.
2. Know the sine, cosine and tangent ratios.
3. Choose the right ratio for a problem.
4. Find a missing side of a right-angled triangle.
Naming the Sides
|
The hypotenuse is opposite the right angle. The opposite side is across from the angle θ. The adjacent side is next to θ and is not the hypotenuse. Move the angle and the opposite and adjacent sides swap. |
Label from the angle you are using. |
SOH CAH TOA
θ is the Greek letter theta, often used for an angle.
|
Ratio |
Formula |
Uses |
|---|---|---|
|
Sine |
sin θ= opp/hyp |
Opposite and hypotenuse |
|
Cosine |
cos θ= adj/hyp |
Adjacent and hypotenuse |
|
Tangent |
tan θ= opp/adj |
Opposite and adjacent |
Finding a Missing Side
The same five steps every time.
|
1 Label Label the sides O, A and H from the given angle. |
2 Choose Tick the side you know and the side you want. The two letters pick the ratio: O and H - sine; A and H - cosine; O and A - tangent. |
3 Write Write the ratio with the numbers in, e.g. sin 35°= x/12. |
4 Rearrange If x is on top, multiply. If x is on the bottom, swap x and the trig value. |
5 Calculate Check your calculator is in degrees (D on the screen), then round. |
The Unknown on Top
|
A right-angled triangle has hypotenuse 15 cm. Angle θ= 42°. Work out the side opposite θ, to 1 decimal place. |
1. Known: H = 15. Wanted: O. O and H means sine
sin 42°= x/15
2. Multiply both sides by 15
x = 15 sin 42°
3. Calculate
x = 10.036…
Answer: 10.0 cm
Using Tangent
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A right-angled triangle has an angle of 55°. The side adjacent to it is 8 cm. Work out the side opposite the 55° angle, to 1 decimal place. |
1. Known: A = 8. Wanted: O. O and A means tangent
tan 55°= x/8
2. Multiply by 8
x = 8 tan 55°
3. Calculate
x = 11.425…
Answer: 11.4 cm
The Unknown on the Bottom
|
A right-angled triangle has an angle of 23°. The side opposite it is 6 cm. Work out the hypotenuse, to 1 decimal place. |
1. Known: O = 6. Wanted: H. O and H means sine
sin 23°= 6/x
2. x is on the bottom, so swap x and sin 23°
x = 6/(sin 23°)
3. Calculate
x = 15.355…
4. Check: the hypotenuse is the longest side
15.4 > 6
Answer: 15.4 cm
Key Terms
|
Hypotenuse The side opposite the right angle; the longest side. |
Opposite The side across from the angle being used. |
|
Adjacent The side next to the angle being used, which is not the hypotenuse. |
Sine (sin) sin θ= opp/hyp. |
|
Cosine (cos) cos θ= adj/hyp. |
Tangent (tan) tan θ= opp/adj. |
Your Task: Trig Relay
12 minutes
|
In pairs. For each triangle, one partner labels the sides and chooses the ratio; the other writes the equation and calculates. Swap roles each time. (a) H = 10, angle 50°, find A. (b) A = 14, angle 36°, find O. (c) A = 25, angle 20°, find H. (d) H = 3, angle 12°, find O. 1. Label O, A, H. 2. Choose the ratio. 3. Rearrange and calculate. |
A good answer shows: (a) 10cos 50°= 6.43 (b) 14tan 36°= 10.17 (c) 25/(cos 20°) = 26.60 (d) 3sin 12°= 0.62, all to 2 decimal places.
Can I...?
☐ Label the hypotenuse, opposite and adjacent sides.
☐ Recall SOH CAH TOA.
☐ Choose the right ratio.
☐ Find a side when it is on the top of the fraction.
☐ Find a side when it is on the bottom of the fraction.
☐ Check my calculator is in degrees.
Summary
✓ Label from the angle: hypotenuse, opposite, adjacent.
✓ SOH CAH TOA picks the ratio.
✓ x on top: multiply. x on the bottom: divide.
✓ Degree mode, then round at the end.
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EXAM FOCUS Triangle ABC is right-angled at B. AB = 7 cm and angle ACB = 40°. Work out the length of BC. Give your answer to 3 significant figures. (3 marks) Write the ratio with the numbers in before you rearrange - it is usually worth a method mark on its own, even if the calculator step goes wrong. |