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?
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