Materi trigonometri Jawab dengan langkah dan cara

Kategori: Matematika - Trigonometri
Kelas: X SMA
Kata Kunci: aturan sinus, aturan cosinus, segitiga
Pembahasan:

Bagian a

Diketahui:
BC = a = 4
AC = b = 10
AB = c = 9

Ditanya:
∠A = ...?
∠B = ...?
∠C = ...?

Jawab:

a² = b² + c² - 2bc cos A
4² = 10² + 9² - 2 . 10 . 9 . cos A
16 = 100 + 81 - 180 . cos A
-165 = -180 . cos A
cos A = -165/-180
cos A = 0,916
∠A = 24°

c/sin C = a/sin A
sin C = sin A/a × c
sin C = 0,407/4 × 9
sin C = 0,915
∠C = 66°

∠B = 180° - (∠A + ∠C)
      = 180° - (24° + 66°)
      = 180° - 90°
      = 90°

Bagian b

Diketahui:
∠A = 120°
AC = b = 3
AB = c = 10

Ditanya:
a = ...?
∠B = ...?
∠C = ...?

Jawab:

a² = b² + c² - 2bc cos A
a² = 3² + 10² - 2 . 3 . 10 . cos 120°
a² = 9 + 100 - 60 . -1/2
a² = 109 + 30
a² = 139
a = 11,789

b/sin B = a/sin A
sin B = sin A/a × b
sin B = 0,866/11,789 × 3
sin B = 0,22
∠B = 13°

∠C = 180° - (∠A + ∠B)
      = 180° - (120° + 13°)
      = 180° - 133°
      = 47°

Bagian c

Diketahui:
∠B = 53°
BC = a = 6
AB = c = 5

Diketahui:
b = ...?
∠A = ...?
∠C = ...?

Jawab:

b² = a² + c² - 2ab cos B
b² = 6² + 5² - 2 . 6 . 5 . cos 53°
b² = 61 - 60 . 0,602
b² =  61 - 36,12
b² = 24,88
b = 4,987

a/sin A = b/sin B
sin A = sin B/b × a
sin A = 0,799/4,987 × 6
sin A = 0,961
∠A = 74°

∠C = 180° - (∠A + ∠B)
      = 180° - (74° + 53°)
      = 180° - 127°
      = 53°