CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Trigonometric Ratios Using Right Angled Triangle

Let A0A1A2A...

Question

Let $A_{0} A_{1} A_{2} A_{3} A_{4} A_{5}$ be a regular hexagon inscribed in a circle of unit radius.The product of the length of the line segments $A_{0} A_{1}, A_{0} A_{2}$ and $A_{0} A_{4}$ is

A

\frac{3}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

3 \sqrt{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

\frac{3 \sqrt{3}}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $3$
$A_{0} A_{1} = 2.1. cos \frac{π}{3} = 2.1. \frac{1}{2} = 1 = A_{1} A_{2}$
$cos \frac{2 π}{3} = \frac{{(A_{0} A_{1})}^{2} + {(A_{1} A_{2})}^{2} - {(A_{0} A_{2})}^{2}}{2 A_{0} A_{1} . A_{1} A_{2}}$
$\Rightarrow cos (π - \frac{π}{3}) = \frac{1 + 1 - {(A_{0} A_{2})}^{2}}{2.1.1}$
$\Rightarrow - cos \frac{π}{3} = \frac{2 - {(A_{0} A_{2})}^{2}}{2}$
$\Rightarrow \frac{- 1}{2} = \frac{2 - {(A_{0} A_{2})}^{2}}{2}$
$\Rightarrow - 1 = 2 - {(A_{0} A_{2})}^{2}$
$\Rightarrow {(A_{0} A_{2})}^{2} = 3$
$∴ A_{0} A_{2} = \sqrt{3} = A_{0} A_{4}$
$∴ A_{0} A_{1} \times A_{0} A_{2} \times A_{0} A_{4} = 1 \times \sqrt{3} \times \sqrt{3} = 3$

Suggest Corrections

thumbs-up

0

Similar questions

A_{0}, A_{1}, A_{2}, A_{3}, A_{4}, A_{5}

be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments

A_{0} A_{1}, A_{0} A_{2}

A_{0} A_{4}

A_{0} A_{1} A_{2} A_{3} A_{4} A_{5}

be a regular hexagon inscribed in a circle of unit radius.Then the product of the length of

A_{0} A_{1} . A_{0} A_{2} . A_{0} A_{4}

A_{0}, A_{1}, A_{2}, A_{3}, A_{4}, A_{5}

be a regular hexagon inscribed in a unit circle with centre at the origin. Then the product of the lengths of the line segments

A_{0} A_{1}, A_{0} A_{2}, A_{0} A_{4}

A_{0}, A_{1}, A_{2}, A_{3}, A_{4}

A_{5}

be the consecutive vertices of a regular hexagon inscribed in a unit circle. The product of the lengths of

A_{0} A_{1},

A_{0} A_{2}

A_{0} A_{4}

x + 1

f (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + \dots + a_{n} = 0

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Trigonometric Functions in a Right Angled Triangle

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Trigonometric Ratios Using Right Angled Triangle

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon