Find correct to the nearest degree, the acute angle formed by the lines y = 2x + 5 and 2y = x – 6
- 76\(^∘\)
- 53\(^∘\)
-
37\(^∘\)
- 14\(^∘\)
The correct answer is: C
Explanation
| tanθ | = | m1 - m2
1 + m1m2 |
y = 2x + 5
m1 = 2
2y = x - 6
| y | = | 1
2 |
x | - | 3 |
| m2 | = | 1
2 |
| tanθ | = | 2 - \(\frac{1}{2}\)
1+2(\(\frac{1}{2}\)) |
tanθ = \(\frac{3}{2}\) ÷ (1+1)
tanθ = \(\frac{3}{2}\) ÷ 2
| tanθ | = | 3
4 |
θ = \(tan^{-1} (\frac{3}{4})\)
θ = 36.87º
θ = 37º