This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Haya Nicholas, hebu tusuluhishe maswali haya ya jiometria. a) Ili kupata eneo la pembetatu ABC, tunatumia fomula ya eneo la pembetatu tunapopewa pande mbili na pembe iliyoko katikati yao. Step 1: Andika fomula ya eneo la pembetatu. Eneo = (1)/(2)ab Ambapo a na b ni urefu wa pande mbili, na ni pembe iliyoko katikati ya pande hizo. Step 2: Badilisha thamani ulizopewa kwenye fomula. Tunapewa AB = 10 cm, BC = 12 cm, na ABC = 30^. Eneo = (1)/(2) × 10 cm × 12 cm × (30^) Step 3: Kokotoa eneo. Tunajua kuwa (30^) = 0.5. Eneo = (1)/(2) × 10 × 12 × 0.5 Eneo = 5 × 12 × 0.5 Eneo = 60 × 0.5 Eneo = 30 cm^2 Eneo la pembetatu ABC ni 30 cm^2. b) Ili kupata urefu wa upande AC, tutatumia Kanuni ya Kosine (Cosine Rule). Step 1: Andika Kanuni ya Kosine. c^2 = a^2 + b^2 - 2ab C Katika kesi hii, tunatafuta AC, kwa hivyo: AC^2 = AB^2 + BC^2 - 2(AB)(BC) ( ABC) Step 2: Badilisha thamani ulizopewa kwenye fomula. Tunapewa AB = 10 cm, BC = 12 cm, na ABC = 30^. AC^2 = (10 cm)^2 + (12 cm)^2 - 2(10 cm)(12 cm) (30^) Step 3: Kokotoa AC^2. Tunajua kuwa (30^) = sqrt(3)2 ≈ 0.8660. AC^2 = 100 + 144 - 2(10)(12) (sqrt(3)2) AC^2 = 244 - 240 (sqrt(3)2) AC^2 = 244 - 120sqrt(3) AC^2 ≈ 244 - 120(1.73205) AC^2 ≈ 244 - 207.846 AC^2 ≈ 36.154 Step 4: Tafuta mzizi wa mraba wa AC^2 ili kupata AC. AC = sqrt(36.154) AC ≈ 6.0128 cm Urefu wa AC ni 6.01 cm (kwa sehemu mbili za desimali). 3 done, 2 left today. You're making progress.