Find, correct to the nearest degree, the acute angle between 3x – y – 5 = 0, and 7x – y – 3 = 0
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10\(^0\)
- 11\(^0\)
- 24\(^0\)
- 27\(^0\)
The correct answer is: A
Explanation
3x - y - 5 = 0, and 7x - y - 3 = 0
Rearrange both equations to the slope-intercept form
y = 3x - 5
y = 7x - 3
So that, m\(_1\) = 3, and m\(_2\) = 7
Tan \(\theta\) = \(\frac{m_2 - m_1}{1 + m_1 m_2}\)
\(\theta\) = tan\(^{-1}\)[\(\frac{m_2 - m_1}{1 + m_1 m_2}\)] = tan\(^{-1}\)[\(\frac{7 - 3}{1 + 7 \times 3}\)]
\(\theta\) = tan\(^{-1}\)[\(\frac{4}{22}\)] = 10.3 ≈ 10º
Thus, the acute angle between the two lines is approximately 10º