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

  81.87°

Step-by-step 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°.

an altitude of 15,000 feet

step-by-step explanation: