Unformatted text preview: ines its shape. If in addition we are given the length of one of the sides
To ﬁnd an exact expression for β , we convert everything back to radians: α = 30◦ = π radians, γ = arcsin
radians and 180◦ = π radians. Hence, β = π − π − arcsin 2 = 56 − arcsin 2 radians ≈ 108.19◦ .
An exact answer for β in this case is β = arcsin 2 − π radians ≈ 11.81◦ .
3 766 Applications of Trigonometry of the triangle, we can then use the Law of Sines to ﬁnd the lengths of the remaining two sides
to determine the size of the triangle. Such is the case in numbers 1 and 2 above. In number 1,
the given side is adjacent to just one of the angles – this is called the ‘Angle-Angle-Side’ (AAS)
case.7 In number 2, the given side is adjacent to both angles which means we are in the so-called
‘Angle-Side-Angle’ (ASA) case. If, on the other hand, we are given the measure of just one of the
angles in the triangle along with the length of two sides, only one of which is adjacent to the given
angle, we are in the ‘Angle-Side-Side’ (ASS) c...
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