TS EAMCET · Maths · Properties of Triangles
If \(a\) and \(b\) respectively represent the leng ths of a side and a diagonal of a regular pentagon that is inscribed in a circle, then \(\frac{b}{a}=\)
- A \(2 \sin \frac{\pi}{5}\)
- B \(2 \cos \frac{\pi}{5}\)
- C \(\cos \frac{\pi}{5}\)
- D \(\sin \frac{\pi}{5}\)
Answer & Solution
Correct Answer
(B) \(2 \cos \frac{\pi}{5}\)
Step-by-step Solution
Detailed explanation
We have, \(a=\) side of pentagon \(b=\) diagonal of regular pentagon \( \begin{aligned} & \angle A C B=\frac{3 \pi}{5} \\ & \angle A C D=\frac{3 \pi}{10} \text { and } \angle C A D=\frac{\pi}{5} \end{aligned} \) In \(\triangle A C D\),…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(\tan A \lt 0\) and \(\tan 2 A=-\frac{4}{3}\), then \(\cos 6 A=\)TS EAMCET 2024 Medium
- The variance of the discrete data \(3,4,5,6,7,8,10,13\) isTS EAMCET 2025 Medium
- If \(f(x)=\frac{1}{x^3} \int_5^x\left(2 u^2-u f^{\prime}(u) d u\right.\), then \(f^{\prime}(5)=\)TS EAMCET 2020 Medium
- \(E_1\) and \(E_2\) are two independent events of a random experiment with \(P\left(E_1\right)=\frac{1}{2}\) and \(P\left(E_1 \cup E_2\right)=\frac{2}{3}\). Then match the items of List-1 with those of List-II.
The correct match is \(\begin{array}{lllllllll}A & \text { B } & \text { C } & \text { D } & \text { A } & \text { B } & \text { C } & \text { D }\end{array}\)TS EAMCET 2020 Medium - \(\int \sqrt{e^x-4} d x\) equalsTS EAMCET 2015 Easy
- The equation of the circle of radius 5 and touching the co-ordinate axes in third quadrant isTS EAMCET 2002 Easy
More PYQs from TS EAMCET
- ' \(\mathrm{x}\) ' \(\mathrm{g}\) of urea (molar mass \(60 \mathrm{gmol}^{-1}\) ) is completely dissolved in ' \(\mathrm{y}\) ' \(\mathrm{g}\) of pure water and the solution boiled at \(373.202 \mathrm{~K}\). If the boiling point of pure water at \(1.013 \mathrm{bar}\) is \(373.15 \mathrm{~K}\), then \(\mathrm{x}: \mathrm{y}\) is \(\left(\mathrm{K}_{\mathrm{b}}\left(\mathrm{H}_2 \mathrm{O}\right)=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)TS EAMCET 2023 Medium
- A venturimeter has a pipe diameter of \(4 \mathrm{~cm}\) and a throat diameter of \(2 \mathrm{~cm}\). Velocity of water in the pipe section is \(10 \mathrm{~m} / \mathrm{s}\). The pressure drop, between pipe section and the throat section is [use density of water \(=1000 \mathrm{~kg} / \mathrm{m}^3\) ]TS EAMCET 2022 Medium
- The sum of the fourth powers of the roots of the equation \(x^3+x+1=0\) isTS EAMCET 2008 Medium
- If a circle passing through \(\mathrm{A}(1,1)\) touches the \(\mathrm{X}\)-axis, then the locus of the other end of the diameter through \(A\) isTS EAMCET 2023 Medium
- In hydrogen atom, the minimum energy required to excite an electron from orbit to the orbit isTS EAMCET 2022 Medium
- If the number of diagonals of a regular polygon is 35 , then the number of sides of the polygon isTS EAMCET 2015 Medium