Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 201008 by Mingma last updated on 27/Nov/23

Answered by mr W last updated on 28/Nov/23

$$\frac{r_n-r_{n+1}}{r_n+r_{n+1}}=\sin \frac{\alpha }{2}=k$$$$\Rightarrow r_{n+1}=\frac{1-k}{1+k}{r}_n$$$$\cos \alpha =\frac{8}{10}=\frac{4}{5}=1-2{\sin }^2\frac{\alpha }{2}$$$$\Rightarrow \sin \frac{\alpha }{2}=\frac{1}{\sqrt{10}}=k$$$$r_1=\frac{6\times 8}{6+8+10}=2$$$$\Rightarrow r_2=\frac{1-\frac{1}{\sqrt{10}}}{1+\frac{1}{\sqrt{10}}}\times 2=\frac{2(11-2\sqrt{10})}{9}$$$$shadedarea=\pi r_2\approx 3.391$$

Commented by Mingma last updated on 28/Nov/23

Nice solution, sir!

Commented by Mingma last updated on 28/Nov/23

Can you show your diagram of explanation?

Commented by mr W last updated on 28/Nov/23

Terms of Service

Privacy Policy

Contact: info@tinkutara.com