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Find the acute angle between L1: y = 0.5x+4 and L2: 3x+y+3=0

I got 45 degrees but I dont know if I am right

User Mkhatib
by
5.6k points

1 Answer

3 votes

Answer:

81.87°

Explanation:

The angle a line makes with the x-axis is equal to the arctangent of its slope. Here, L1 makes an angle of arctan(0.5) = 26.57° with the x-axis; L2 makes an angle of arctan(-3) = -71.57° with the x-axis. The difference between these angles is ...

26.57° -(-71.57°) ≈ 98.13° . . . . . . all numbers rounded to 2 decimal places

This is an obtuse angle, so the acute angle is ...

180° -98.13° = 81.87°

_____

You can also use the trig formula for the difference of angles. Tan(α) is the slope of the first line, 0.5. Tan(β) is the slope of the second line, -3.

tan(α-β) = (tan(α)-tan(β))/(1 +tan(α)tan(β))

tan(angle) = (0.5 -(-3))/(1 +(0.5)(-3)) = 3.5/(-0.5) = -7

angle = arctan(-7) = -81.87°

The angle between the two lines is 81.87°.

Find the acute angle between L1: y = 0.5x+4 and L2: 3x+y+3=0 I got 45 degrees but-example-1
User Jeremy Wong
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4.9k points