Unformatted text preview: grees, we ﬁnd α ≈ 55.15◦ . Now
that we have the measure of angle α, we could ﬁnd the measure of angle β using the fact that α
and β are complements so α + β = 90◦ . Once again, we opt to use the data given to us in the
problem. According to Theorem 10.4, we have that sin(β ) = 7 so β = arcsin 7 radians and we
have β ≈ 34.85◦ .
A few remarks about Example 11.2.1 are in order. First, we adhere to the convention that a lower
case Greek letter denotes an angle1 and the corresponding lowercase English letter represents the
side2 opposite that angle. Thus, a is the side opposite α, b is the side opposite β and c is the side
opposite γ . Taken together, the pairs (α, a), (β, b) and (γ, c) are called angle-side opposite pairs.
Second, as mentioned earlier, we will strive to solve for quantities using the original data given in
the problem whenever possible. While this is not always the easiest or fastest way to proceed, it
2 as well as the measure of said angle
as well as the length of said sid...
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