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1 Pure Mathematics

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Question 869

Figure 1 below shows the right-angled triangle ABCABCABC, in which the angle at C C\,C is a right angle and AB=5AB = 5AB=5 cm.

Figure for question 1

The angle BAC BAC\,BAC is θ\thetaθ, where θ \theta\,θ is measured in radians.

a.

Given that θ \theta\,θ is small, show that AC≈5−5θ22\displaystyle AC \approx 5 - \frac{5\theta^2}{2}AC≈5−25θ2​.

[2]
b.

Hence find the length of AC AC\,AC when θ=0.1\theta = 0.1θ=0.1, giving your answer to four decimal places.

[2]
Markscheme

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