急 ! F4 Basic Trigonometry eam1

1.
AB² = AC² + BC² (Pythagorean theorem)
5² = AC² + 4²
AC = 3

sin(180° - θ) = AC/AB
sinθ =3/5

cos(180° - θ) = BC/AB
-cosθ = 4/5
cosθ =-4/5

tan(180° - θ) = AC/BC
-tanθ = 3/4
tanθ =-3/4


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2.
AB/sinC = AC/sinB (sine law)
4/sinC = 3/sin30°
sinC = 4 sin30°/3
sinC = 4 * (1/2)/3
sinC = 2/3

A + B + C = 180° (∠ sum of Δ)
C = 180° - (A + B)

Since sinC = 2/3
then sin[180° - (A + B)] = 2/3
sin(A + B) = 2/3