Find the acute angle between the two lines y = 2x + 1 and y = 3x - 4 using the tangent angle formula.
Answer and explanation
Correct answer: D. arctan(1/7) approx 8.13°
- Step 1: Identify slopes of lines: m1 = 2 and m2 = 3.
- Step 2: Apply formula: tan(theta) = |(m2 - m1) / (1 + m1 * m2)|.
- Step 3: Substitute: tan(theta) = |(3 - 2) / (1 + (2)(3))| = |1 / (1 + 6)| = 1/7.
- Step 4: Acute angle theta = arctan(1/7).
Answer
arctan(1/7) approx 8.13°.
Why not the others: 'arctan(5)' forgets the denominator (1 + m1m2); '45°' would require tan(theta) = 1; 'arctan(1/5)' calculates 1 + 22.
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