Answer:
2tanθ -2 = y
Step-by-step explanation:
First, to make things a little simpler, we can say that the point between C and B is D, so BD = y
We are given that ∠ADC = 45° , and ∠ACD = 90°. Because the angles of a triangle add up to 180 degrees, we can say
∠CAD + ∠ACD + ∠ADC = 180°
∠CAD + 90 + 45 = 180
∠CAD = 45°
In a 45/45/90 degree triangle, we can say that the two non-hypotenuse sides are the same. The hypotenuse is opposite of the right angle, so in this triangle, it would be AD. Therefore, we can say that AC = CD = 2
Because BC = CD + DB , we can say that
BC = CD + DB
BC = 2 + y
y = BC -2
Therefore, if we know BC, we can solve for y.
We want to solve for BC given
- the angle opposite of it (θ)
- the side adjacent to the angle (AC).
One equation that fits this is
tanθ = opposite/adjacent
tanθ = BC/AC
tanθ = (2+y)/2
multiply both sides by 2 to remove a denominator
2 tanθ=2+y
subtract 2 from both sides to isolate th y
2tanθ -2 = y
