GCSE Maths | Trigonometry
What is the sine rule?
a/sin(A) = b/sin(B)
sin(A)/a = sin(B)/b
Question 1 - finding a length using the sine rule
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a) $x = 6.39$ cm
b) $x = 6.65$ cm
c) $x = 60.5$ mm
Question 2 - finding an angle using the sine rule
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a) $\theta = 37.1°$
b) $\theta = 26.8°$
c) $\theta = 40.5°$
What is the cosine rule?
a2 = b2 + c2 - 2bc cos(A)
Question 3 - finding a length using the cosine rule
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a) $x = 9.17$ cm
b) $x = 30.41$ cm
c) $x = 36.67$ mm
How do you rearrange the cosine rule to make cos(A) the subject?
a2 = b2 + c2 - 2bc cos(A)
2bc cos(A) = b2 + c2 - a2
cos(A) = (b2 + c2 - a2)/2bc
Question 4 - finding an angle using the cosine rule
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a) $\theta = 49.5°$
b) $\theta = 60.0°$
c) $\theta = 87.2°$
What is the area of any triangle?
Area = (1/2) ab sin(C)
Question 5 - finding the area of any triangle
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a) $45.0$ cm²
b) $156.32$ cm²
c) $52.62$ cm²
Question 6 - using the area of a triangle to work out a missing length
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a) $y = 8.51$ cm
b) $y = 6.96$ cm
c) $y = 7.95$ cm
Question 7 - using the area of a triangle to work out a missing angle
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a) $x = 78.9°$
b) $x = 31.6°$
c) $x = 30.0°$
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