In the triangle ABC, AC=2cm, AB=x cm and angle ABC=π/2 rad.

Question

1. Given that angle BAC=ϴ rad, and that ϴ is a sufficiently small angle, show that x≈ a + bϴ^2, where a and b are constants to be determined.
2. For this part, ϴ is not assumed to be a small angle. The point N lies on AB such that the ratio of AN to AB is 2:5. By showing that (CN)^2= 4 - 0.64x^2, find the constants c and d such that when x is small, cos ∠ACN≈ c + dx^2.

I've done Q1 and half of Q2. I've shown the equation but can't figure out how to find constants c and d. I tried using cosine rule but couldn't get an answer.. Can someone help me?

Answer 1

You now have expressions for AN and NC

Using the law of cosines,

AN^2 = CN^2 + 2^2 - 2*CN*2 cos∠ACN

Answer 2

The maximum angle of the sun above the horizon for a small town in Ontario was recorded on the 21st of each month and is displayed in the table below. Create an equation to model the data.