Asked by John
In the triangle ABC, AC=2cm, AB=x cm and angle ABC=π/2 rad.
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?
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?
Answers
Answered by
Steve
You now have expressions for AN and NC
Using the law of cosines,
AN^2 = CN^2 + 2^2 - 2*CN*2 cos∠ACN
Using the law of cosines,
AN^2 = CN^2 + 2^2 - 2*CN*2 cos∠ACN
Answered by
kaiya
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.
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