The line y = -3 is a horizontal line. The perpendicular line will be vertical, so will have an equation of the form
x = c
for some constant c.
You want the vertical line to go through the point (4, -6), so the required value of c is the x-value of that point: 4
Your equation is
x = 4
93% because you completed the original set of 100% with the 93/7 day. You can practically restart the count and have again a 93% chance, as you originally had.
Answer:
(a) α = 60°, β = 30°
(b) α ≈ 67.4°, β ≈ 22.6°
Step-by-step explanation:
I'll do (a) and (b) as examples. Make sure your calculator is set to degrees, not radians.
(a) For α, we're given the opposite and adjacent sides, so use tangent.
tangent = opposite / adjacent
tan α = √300 / 10
tan α = √3
α = 60°
Since angles of a triangle add up to 180°, we know that β = 30°. But we can use tangent again to prove it:
tan β = 10 / √300
tan β = 1 / √3
tan β = √3 / 3
β = 30°
(b) For α, we're given the adjacent side and the hypotenuse. So use cosine.
cos α = adjacent / hypotenuse
cos α = 15 / 39
cos α = 5 / 13
α ≈ 67.4°
Again, we know that β = 22.6°, but let's show it using trig. We're given the opposite side and hypotenuse, so use sine:
sin β = 15 / 39
sin β = 5 / 13
β ≈ 22.6°
