Question

find the slope of a line whose inclination is 105

Answer 1

slope m = tan theta
m = tan 105°
m = tan (180°-105°)
m = tan 75°
m = tan(45°+30°)
m = (tan45°+tan30°) / 1 - (tan45°)(tan30°)
m = (1+1/√3) / [1 - (1)(1/√3)]
m = [(√3+1) / √3] - [(√3-1) / √3]
m = (√3+1) / (√3-1)
m = [(√3+1)(√3+1)] / [(√3-1)(√3+1)]
m = (√3+1)² / [(√3)²- (1)²]
m = (3+1+2√3) / 2
m = (4+2√3) / 2
m = 2+√3
therefore, the slope of the line is (2+√3)

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