Find the third angle in triangle ABC.

April 13, 2026Mathematics

ScanSolve AI Answer

April 13, 2026

Answer

35.90

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Step 1: Find the third angle in triangle ABC. The sum of angles in a triangle is $180^\circ$ . $\angle ACB = 180^\circ - \angle ABC - \angle CAB$ $\angle ACB = 180^\circ - 80^\circ - 45^\circ$ $\angle ACB = 55^\circ$

Step 2: Apply the Sine Rule to find BC. The Sine Rule states that for a triangle with sides a, b, c and opposite angles A, B, C: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ In triangle ABC, we want to find side BC (let's call it $a$ ), and we know angle CAB (A). We also know side AC (let's call it $b$ ) and angle ABC (B). $\frac{BC}{\sin(\angle CAB)} = \frac{AC}{\sin(\angle ABC)}$ Substitute the given values: $\frac{BC}{\sin(45^\circ)} = \frac{50}{\sin(80^\circ)}$ Solve for BC: $BC = \frac{50 \times \sin(45^\circ)}{\sin(80^\circ)}$ $BC = \frac{50 \times 0.7071}{0.9848}$ $BC = \frac{35.355}{0.9848}$ $BC \approx 35.90 units$

The length of BC is approximately $\boxed{35.90}$ .

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Quick Answer

Hey, good to see you again. Step 1: Find the third angle in triangle ABC.

Asked on April 13, 2026Mathematics

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 AnswerAnswered on April 13, 2026

Hey, good to see you again. Step 1: Find the third angle in triangle ABC. The sum of angles in a triangle is 180^. ACB = 180^ - ABC - CAB ACB = 180^ - 80^ - 45^ ACB = 55^ Step 2: Apply the Sine Rule to find BC. The Sine Rule states that for a triangle with sides a, b, c and opposite angles A, B, C: (a)/( A) = (b)/( B) = (c)/( C) In triangle ABC, we want to find side BC (let's call it a), and we know angle CAB (A). We also know side AC (let's call it b) and angle ABC (B). (BC)/(( CAB)) = (AC)/(( ABC)) Substitute the given values: (BC)/((45^)) = (50)/((80^)) Solve for BC: BC = (50 × (45^))/((80^)) BC = (50 × 0.7071)/(0.9848) BC = (35.355)/(0.9848) BC ≈ 35.90 units The length of BC is approximately 35.90. Send me the next one 📸

Asked on April 13, 2026Mathematics

ScanSolve AI AnswerAnswered on April 13, 2026

Hey, good to see you again. Step 1: Find the third angle in triangle ABC. The sum of angles in a triangle is 180^. ACB = 180^ - ABC - CAB ACB = 180^ - 80^ - 45^ ACB = 55^ Step 2: Apply the Sine Rule to find BC. The Sine Rule states that for a triangle with sides a, b, c and opposite angles A, B, C: (a)/( A) = (b)/( B) = (c)/( C) In triangle ABC, we want to find side BC (let's call it a), and we know angle CAB (A). We also know side AC (let's call it b) and angle ABC (B). (BC)/(( CAB)) = (AC)/(( ABC)) Substitute the given values: (BC)/((45^)) = (50)/((80^)) Solve for BC: BC = (50 × (45^))/((80^)) BC = (50 × 0.7071)/(0.9848) BC = (35.355)/(0.9848) BC ≈ 35.90 units The length of BC is approximately 35.90. Send me the next one 📸