△PQR dengan sisi QR= 4, PR=5 , ∠P=75°, dan ∠R=30° Tentukan panjang PQ dan ∠Q!

Jawaban yang benar adalah PQ = 2(√6 - √2) dan ∠Q = 75° Pembahasan : Pada segitiga PQR, berlaku : p/sin P = q/sin Q = r/sin R p = QR q = PR r = PQ Jumlah sudut dalam segitiga = 180° P + Q + R = 180° sin (a + b) = sin a cos b + cos a sin b QR = p = 4 PR = q = 5 PQ = r ∠P = 75° ∠R = 30° P + Q + R = 180° 75° + Q + 30° = 180° Q = 180° - 75° - 30° Q = 75° sin 75° = sin (45°+30°) = sin 45° cos 30° + cos 45° sin 30° = (1/2)√2 · (1/2) √3 + (1/2)√2 · (1/2) = (1/4) √(2·3) + (1/4) √2 = (1/4) (√6 + √2) r/sin R = p/sin P r/sin 30° = 4/sin 75° r · sin 75° = sin 30° · 4 r · (1/4)(√6 + √2) = (1/2) · 4 (dikali 4) r (√6 + √2) = 8 r = 8/(√6 + √2) r = 8/(√6 + √2) · (√6 - √2)/(√6 - √2) r = 8(√6 - √2)/(√6 + √2)(√6 - √2) r = 8(√6 - √2)/(6 - 2) r = 8(√6 - √2)/4 r = 2(√6 - √2) Jadi diperoleh panjang PQ = 2(√6 - √2) dan ∠Q = 75°