Question

Hitunglah luas masing-masing segitiga tersebut! TRIGONOMETRI KELAS 10
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Answer 1

Verified answer

• Luas ΔABC (gbr. 7.35) = 3√3 cm².
• Luas ΔABC (gbr. 7.36) = ½·(9√3 + 3√7) cm².

 

Penjelasan dengan langkah-langkah

Trigonometri

Luas ΔABC (gambar 7.35)

L = ½·AB·AC·sin ∠A
⇔ L = ½·3·4·sin 60°
⇔ L = 6·½√3
⇔ L = 3√3 cm²

Luas ΔABC (gambar 7.36)

Aturan sinus:
AB/sin ∠C = BC/sin ∠A
⇔ sin ∠C = (AB/BC) sin ∠A
⇔ sin ∠C = (6/4) sin 30° = (3/2)·½ = 3/4
⇔ cos ∠C = √(1 – 9/16) = ¼√7

L = ½·alas·tinggi
⇔ L = ½·AC·t
⇔ L = ½·(AB cos ∠A + BC cos ∠C)·AB sin ∠A
⇔ L = ½·(AB² sin ∠A cos ∠A + AB·BC·sin ∠A cos ∠C)
⇔ L = ½·(AB² ½·sin (2·∠A) + AB·BC·sin ∠A cos ∠C)
⇔ L = ½·(6²·½·sin 60° + 6·4·sin 30°·¼√7)
⇔ L = ½·(9√3 + 3√7) cm²