Question

Diketahui sebuah segitiga PQR dengan panjang sisi p = 3√2. Besar sudut di p = 45° dan q = 30°. Hitunglah panjang sisi p dan q serta sudut di r !​

Answer 1

Verified answer

trigonometri

aturan sinus

p/sin P = q/sin Q = r/sin R

P + Q + R = 180°

45° + 30° + R = 180°

R = 105°

p/sin 45° = q/sin 30°

q = p × sin 30° / sin 45°

q = 3√2 × (1/2) / (1/2 √2)

q = 3 satuan

sin R

= sin 105°

= sin (60 + 45)°

= sin 60° cos 45° + cos 60° sin 45°

= 1/2 √3 . 1/2 √2 + 1/2 . 1/2 √2

= 1/4 (√6 + √2)

r/sin R = q/sin Q

r = q × sin 105° / sin 30°

r = 3 × (1/4 (√6 + √2)) / (1/2)

r = 3/2 (√6 + √2) satuan