Jawab:

cos C = 3/5

Penjelasan dengan langkah-langkah:

Diketahui segitiga ABC merupakan segitiga lancip. Panjang sisi AB = 10 cm dan AC = 12 cm. Jika nilai sin B = 4/5, nilai cos C = ...?

Jawab:

AC/sin ∠B = AB/sin C

⇔ AC × sin ∠C = AB × sin B

⇔ 12 × sin ∠C = 10 × ⁴/₅

⇔ 12 × sin ∠C = 8

⇔ sin ∠C = 8/12

⇔ sin ∠C = 2/3

AC/sin ∠B = BC/sin A

⇔ AC ×  sin A = BC × sin B

⇔ 12 × ²/₃ = BC × ⁴/₅

⇔ 8 = ⁴/₅ BC

⇔ BC = 8 × ⁵/₄

⇔ BC = 10 cm

AB² = AC² + BC² - 2 × AC × BC × cos C

10² = 12² + 10² - 2 × 12 × 10 × cos C

100 = 144 + 100 - 240 × cos C

-144 = -240 × cos C

cos C = 3/5