The Sine Rule C Mc Minn SOHCAHTOA can
- Slides: 12
The Sine Rule C. Mc. Minn
SOH/CAH/TOA can only be used for right-angled triangles. The Sine Rule can be used for any triangle: C b The sides are labelled to match their opposite angles A The Sine Rule: a = sin. A a B c b = sin. B c sin. C
We use the Sine Rule when: We have two angles and a side OR We have two sides and the non-included angle (this is the ambiguous case)
A Example 1: Find the length of BC 76º c 7 cm b 63º C a a B c = sin. A sin 76º × x sin. C 7 sides to the Drawxarrows from the = × sin 76º opposite help decide sin 76º angles tosin 63º which parts of the sine rule to use. 7 x = × sin 76º sin 63º x = 7. 6 cm
P Example 2: Find the length of PR 82º x r 43º q 55º Q p p 15 cm R q = sin. P sin. Q Draw 15 arrows from thexsides to the sin 43º × opposite angles = to help decide × sin 43º sin 82º which parts of the sine rule to use. 15 = x sin 43º × sin 82º x = 10. 33 cm
B 1. 3. G 2. F 53º A 13 x 5. 5 62º 28º D 5 c m cm 130º E x 8. 0 P 10. 7 x 37º 66º 35. 3 x 63º 76º H 26 mm C 4. 41º R m c 2. 5 5. 61º 6. 57º 77º 10 m x 5. 2 35º 62º 12 c Q 65º x 6. 6 m 7. 85º 6 km 86º x 6. 9 I
Remember: • • Draw a diagram Label the sides Set out your working exactly as you have been shown Check your answers regularly and ask for help if you need it
Finding an Angle The Sine Rule can also be used to find an angle, but it is easier to use if the rule is written upside-down! Alternative form of the Sine Rule: sin. A a = sin. B = b sin. C c
C Example 1: b Find the size of angle ABC 6 cm a 4 cm xº 72º A sin. B = a 4× 4× B c b sin 72º sin xº Draw arrows from the sides = × 4 to the 6 opposite angles 4 to help decide which parts of the sine rule to use. sin 72º = sin xº 6 sin xº = 0. 634 x = sin-1 0. 634 = 39. 3º
P Example 2: Find the size of angle PRQ 85º 7 c m q r xº R p 8. 2 cm sin. P sin. R = p sin 85º 7× Q sin xº = 8. 2 r 7 × 7 sin 85º 7× = 8. 2 sin xº = 0. 850 x = sin-1 0. 850 = 58. 3º
7. 6 cm 82º 66. 6° xº 37. 6° xº 45. 5° xº 6 cm 5. cm xº 31. 0° 33º 5. 2 6. m 8. 8 c 6 km 5. 5 cm 27º 3. 5 km xº 51. 1° cm xº 57. 7° 9. 5 m 4. 6. 5 105º 2 47º 3. cm 2. 8. 5 cm 1. 8 m 7. 70º 52. 3º (←Be careful!→) 74º 9 m m 22. 9º 92. 1° xº 7 mm
Remember: • • Draw a diagram Label the sides Set out your working exactly as you have been shown Check your answers regularly and ask for help if you need it
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