ekamiaww
1) AC / sin B = BC / sin A 5 / sin B = 4 / (3/5) sin B = (5 x 3/5) / 4 sin B = 3/4 sin B = depan / miring depan = 3 cm miring = 4 cm samping² = miring² - depan² = 4² - 3² = 16 - 9 samping² = 5 samping = √5 cos B = samping / miring cos B = √5/4
2) PR / sin Q = QR / sin P 10 / sin Q = 20 / sin 45 10 / sin Q = 20 / (1/2 √2) sin Q = (10 x 1/2 √2) / 20 sin Q = √2/4 sin Q = depan/miring depan = √2 cm miring = 4 cm samping² = miring² - depan² = 4² - (√2)² = 16 - 2 = 14 sampng = √14 tan Q = depan/samping tan Q = √2 / √14 = 1 / √7 x √7 / √7 = 1/7 √7
5) luas Δ PQR = 1/2 x PQ x PR x sin P = 1/2 x 6 x 10 x sin 135 = 1/2 x 60 x 1/2 √2 = 15 √2 cm²
8) luas segi-n beraturan = 1/2 x r² x sin (360/n) luas segi-12 beraturan = 1/2 x 8² x sin (360/12) = 1/2 x 64 x sin 30 = 1/2 x 64 x 1/2 = 16 cm²
5 / sin B = 4 / (3/5)
sin B = (5 x 3/5) / 4
sin B = 3/4
sin B = depan / miring
depan = 3 cm
miring = 4 cm
samping² = miring² - depan²
= 4² - 3²
= 16 - 9
samping² = 5
samping = √5
cos B = samping / miring
cos B = √5/4
2) PR / sin Q = QR / sin P
10 / sin Q = 20 / sin 45
10 / sin Q = 20 / (1/2 √2)
sin Q = (10 x 1/2 √2) / 20
sin Q = √2/4
sin Q = depan/miring
depan = √2 cm
miring = 4 cm
samping² = miring² - depan²
= 4² - (√2)²
= 16 - 2
= 14
sampng = √14
tan Q = depan/samping
tan Q = √2 / √14 = 1 / √7 x √7 / √7 = 1/7 √7
5) luas Δ PQR = 1/2 x PQ x PR x sin P
= 1/2 x 6 x 10 x sin 135
= 1/2 x 60 x 1/2 √2
= 15 √2 cm²
8) luas segi-n beraturan = 1/2 x r² x sin (360/n)
luas segi-12 beraturan = 1/2 x 8² x sin (360/12)
= 1/2 x 64 x sin 30
= 1/2 x 64 x 1/2
= 16 cm²
semoga membantu ya :)