Question

Tentukan luas kedua segitiga tersebut!
soal trigonometri kelas 10​

Answer 1

Verified answer

trigonometri

aturan sinus

a/sin A = c/sin C

a = c × sin A/sin C

a = 5 sin 45° / sin 60°

a = 5 × (1/2 √2)/(1/2 √3)

a = 5 × √2 / √3

a = 5/3 √6 satuan

A + B + C = 180°

45° + B + 60° = 180°

B = 75°

sin 75°

= sin (45 + 30)°

= sin 45° cos 30° + cos 45° sin 30°

= 1/4 √6 + 1/4 √2

= (√6 + √2)/4

Luas ∆ABC

= 1/2 × AB × BC × sin B

= 1/2 × c × a × sin 75°

= 1/2 × 5 × 5/3 √6 × (√6 + √2)/4

= 25/24 (6 + √12)

= 25/24 (6 + 2√3)

= 25/4 + 25/12 √3

= (75 + 25√3)/12 satuan luas