Diketahui segitiga ABC dengan AC=10cm, sudut B=45° dan sudut A=30°, panjang BC adalah…A.10√2

Pertanyaan:

Diketahui segitiga ABC dengan AC=10cm, sudut B=45° dan sudut A=30°, panjang BC adalah…A.10√2 cm
B.5√6 cm
C.5√2 cm
D.5/2.√6 cm
E.5/2.√2 cm
Dijawab dgn caranya ya teman2

Berdasarkan soal, diketahui informasi berikut:

Untuk mencari panjang sisi jika diketahui satu sisi dan dua sudut yang berhadapan, kita menggunakan Aturan Sinus : B C sin A = A C sin B the fraction with numerator cap B cap C and denominator sine cap A end-fraction equals the fraction with numerator cap A cap C and denominator sine cap B end-fraction B C s i n A = A C s i n B

Masukkan nilai yang diketahui ke dalam rumus: B C sin 30 ∘ = 10 sin 45 ∘ the fraction with numerator cap B cap C and denominator sine 30 raised to the composed with power end-fraction equals the fraction with numerator 10 and denominator sine 45 raised to the composed with power end-fraction B C s i n 3 0 ∘ = 1 0 s i n 4 5 ∘ B C = 10 ⋅ sin 30 ∘ sin 45 ∘ cap B cap C equals the fraction with numerator 10 center dot sine 30 raised to the composed with power and denominator sine 45 raised to the composed with power end-fraction B C = 1 0 ⋅ s i n 3 0 ∘ s i n 4 5 ∘ B C = 10 ⋅ 1 2 1 2 2 cap B cap C equals the fraction with numerator 10 center dot one-half and denominator one-half the square root of 2 end-root end-fraction B C = 1 0 ⋅ 1 2 1 2 2 √ B C = 5 1 2 2 cap B cap C equals the fraction with numerator 5 and denominator one-half the square root of 2 end-root end-fraction B C = 5 1 2 2 √ B C = 10 2 cap B cap C equals the fraction with numerator 10 and denominator the square root of 2 end-root end-fraction B C = 1 0 2 √ Rasionalkan penyebut dengan mengalikan 2 2 the fraction with numerator the square root of 2 end-root and denominator the square root of 2 end-root end-fraction 2 √ 2 √ : B C = 10 2 ⋅ 2 2 = 10 2 2 = 5 2 cap B cap C equals the fraction with numerator 10 and denominator the square root of 2 end-root end-fraction center dot the fraction with numerator the square root of 2 end-root and denominator the square root of 2 end-root end-fraction equals the fraction with numerator 10 the square root of 2 end-root and denominator 2 end-fraction equals 5 the square root of 2 end-root B C = 1 0 2 √ ⋅ 2 √ 2 √ = 1 0 2 √ 2 = 5 2 √

Panjang B C cap B cap C B C adalah 5 2 cm 5 the square root of 2 end-root cm 5 2 √ c m . Jadi, jawaban yang benar adalah C .