Question

Trigonometri kelas XI

Answer 1

Verified answer

∆ABC

sudut A = 75°
sudut B = 60°
sudut C = 180° - (75° + 60°) = 45°
AB = 20 cm

Aturan sinus
BC/sin A = AC/sin B = AB/sin C

BC/sin A = AB/sin C
BC/sin 75° = 20/sin 45°
BC = 20 sin (45 + 30) / sin 45

sin (45 + 30)
= sin 45 cos 30 + cos 45 sin 30
= 1/4 √6 + 1/4 √2
= 1/2 √2 (1/2 √3 + 1/2)

BC = 20 . 1/2 √2 (1/2 √3 + 1/2) / 1/2 √2
BC = 20(1/2 √3 + 1/2)
BC = 10(1 + √3) cm

Answer 2

Verified answer

Trigonometri

AB = 20 cm
<B = 60°
<A = 75°

BC?

<C = 180-60-75
<C = 45°

Gunakan aturan sinus

BC/sin A = AB/sin C
BC/sin 75 = 20/sin 45

sin 75
= sin (45 +30)
= sin 45 cos 30 + sin30 cos 45
=( ((√2)/2 ) (√3)/2))) + (1/2) ( √2/2)
= ( (√6) ) /4 + (√2 )/4
= (√6 + √2)/4

sin 45 = (√2/2)

BC / ((√6 + √2)/4) = 20 / (√2/2)
BC . (√2)/2 = 20 . ( ( √6 + √2))/4
BC = (5√6 + 5√2) x 2/√2
BC = (5√6 + 5√2 ) x √2
BC = 10 + 5√12 cm
BC = 10 + 10√3 cm
BC =10(1 + √3) cm