In the diagram, $$\(A B C\)$$ is an isosceles triangle with $$\(A B=B C=r \mathrm{~cm}\)$$ and angle $$\(B A C=\theta\)$$ radians. The point $$\(D\)$$ lies on $$\(A C\)$$ and $$\(A B D\)$$ is a sector of a circle with centre $$\(A\)$$. In the case where $$\(r=10\)$$ and $$\(\theta=0.6\)$$, find the perimeter of the shaded region. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w20_qp_12 Year：2020 Question No：8(b)
Answer:
\(\operatorname{Arc} B D=r \theta=6 \mathrm{~cm}\)
\(A C=2 r \cos \theta=(2 \times 10 \cos 0.6=20 \cos 0.6=16.506)\)
or \(\sqrt{\left(2 r^{2}-2 r^{2} \cos (\pi-2 \theta)\right)}\) or \(\frac{r \times \sin (\pi-2 \theta)}{\sin \theta}\)
\(D C=2 r \cos \theta-r\) or \(\sqrt{\left(2 r^{2}-2 r^{2} \cos (\pi-2 \theta)\right)}-r(=6.506)\)
\((\) Perimeter \(=10+6+6.506=) 22.5\)
\(A C=2 r \cos \theta=(2 \times 10 \cos 0.6=20 \cos 0.6=16.506)\)
or \(\sqrt{\left(2 r^{2}-2 r^{2} \cos (\pi-2 \theta)\right)}\) or \(\frac{r \times \sin (\pi-2 \theta)}{\sin \theta}\)
\(D C=2 r \cos \theta-r\) or \(\sqrt{\left(2 r^{2}-2 r^{2} \cos (\pi-2 \theta)\right)}-r(=6.506)\)
\((\) Perimeter \(=10+6+6.506=) 22.5\)
Knowledge points:
1.4.2 use the formulae in solving problems concerning the arc length and sector area of a circle (Including calculation of lengths and angles in triangles and areas of triangles.)
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download