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
Hapa kuna suluhisho la swali la boti: Swali: Boti katika nukta R inaonekana kutoka nukta mbili P na Q ambazo ziko umbali wa kilomita 3. Tafuta PR na QR; ikiwa RPQ = 84^ na PQR = 67^. Step 1: Tafuta ukubwa wa pembe ya tatu katika pembetatu PQR. Jumla ya pembe katika pembetatu ni 180^. PRQ = 180^ - ( RPQ + PQR) PRQ = 180^ - (84^ + 67^) PRQ = 180^ - 151^ PRQ = 29^ Step 2: Tumia Kanuni ya Saini (Sine Rule) kupata urefu wa PR. Kanuni ya Saini inasema (a)/( A) = (b)/( B) = (c)/( C). Tunajua PQ = 3 km, RPQ = 84^, PQR = 67^, na PRQ = 29^. Ili kupata PR (upande unaopingana na PQR), tunatumia: (PR)/(( PQR)) = (PQ)/(( PRQ)) (PR)/((67^)) = (3)/((29^)) PR = (3 × (67^))/((29^)) PR = (3 × 0.9205)/(0.4848) PR = (2.7615)/(0.4848) PR ≈ 5.696 km Step 3: Tumia Kanuni ya Saini kupata urefu wa QR. Ili kupata QR (upande unaopingana na RPQ), tunatumia: (QR)/(( RPQ)) = (PQ)/(( PRQ)) (QR)/((84^)) = (3)/((29^)) QR = (3 × (84^))/((29^)) QR = (3 × 0.9945)/(0.4848) QR = (2.9835)/(0.4848) QR ≈ 6.154 km Majibu ya mwisho ni: PR ≈ 5.70 km, QR ≈ 6.15 km Last free one today — make it count tomorrow, or type /upgrade for unlimited.