Construct-an-angle-whose-sine-is-3-2-5-

Question Number 206971 by MATHEMATICSAM last updated on 02/May/24

Construct an angle whose sine is

\frac{3}{2 + \sqrt{5}} .

Answered by Rasheed.Sindhi last updated on 02/May/24

\sin θ = \frac{3}{2 + \sqrt{5}}

∙ θ i s a n a n g l e o f a r i g h t t r i a n g l e

w h o s e h y p o t e n u s e i s 2 + \sqrt{5} a n d

o p p o s i t e s i d e i s 3

∙ \sqrt{5} i s a h y p o t e n u s e o f a r i g h t

t r i a n g l e h a v i n g l e g s 2 a n d 1

▸ D r a w a r i g h t t r i a n g l e h a v i n g

l e g s 2 a n d 1 . E x t e n d i t s h y p o t e n u s e

\sqrt{5} t o \sqrt{5} + 2 .

D r a w s e m i c i r c l e o n l i n e s e g m e n t

\overset{―}{AB} h a v i n g m e a s r e \sqrt{5} + 2

C u t o f f 3 u n i t s f r o m B o f s e m i c i r c l e

a t C .

J o i n C t o A a n d B

∠ BAC i s a r e q u i r e d a n g l e .

Commented by Rasheed.Sindhi last updated on 02/May/24

Commented by MATHEMATICSAM last updated on 02/May/24

Thank you!