Math Question and Answers


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 89580 by jagoll last updated on 18/Apr/20

	Answered by $@ty@m123 last updated on 18/Apr/20
	$((BD)/(sin x))=((AD)/(sin {180−(x+84+42)})) ((BD)/(sin x))=((AD)/(sin (54−x))) ...(1) ((BD)/(sin 84))=((BC)/(sin {180−(84+42)})) ((BD)/(sin 84))=((AD)/(sin 54)) ...(2) From (1) &(2), ((sin (54−x))/(sin x))=((sin 54)/(sin 84)) ((sin (54−x)+sin x)/(sin (54−x)−sin x))=((sin 54+sin 84)/(sin 54−sin 84)) ((2sin 27cos (27−x))/(2cos 27sin (27−x)))=((2sin 69cos 15)/(2cos 69(−sin 15))) ((tan 27)/(tan (27−x)))=−((tan 69)/(tan 15)) tan (x−27)=((tan 27)/(tan 69))×tan 15 tan (x−27)≈tan 3^o x≈30^o$
	$\frac{B D}{\sin x} = \frac{A D}{\sin {180 - (x + 84 + 42)}}$ $\frac{B D}{\sin x} = \frac{A D}{\sin (54 - x)} . . . (1)$ $\frac{B D}{\sin 84} = \frac{B C}{\sin {180 - (84 + 42)}}$ $\frac{B D}{\sin 84} = \frac{A D}{\sin 54} . . . (2)$ $F r o m (1) & (2),$ $\frac{\sin (54 - x)}{\sin x} = \frac{\sin 54}{\sin 84}$ $\frac{\sin (54 - x) + \sin x}{\sin (54 - x) - \sin x} = \frac{\sin 54 + \sin 84}{\sin 54 - \sin 84}$ $\frac{2 \sin 27 \cos (27 - x)}{2 \cos 27 \sin (27 - x)} = \frac{2 \sin 69 \cos 15}{2 \cos 69 (- \sin 15)}$ $\frac{\tan 27}{\tan (27 - x)} = - \frac{\tan 69}{\tan 15}$ $\tan (x - 27) = \frac{\tan 27}{\tan 69} \times \tan 15$ $\tan (x - 27) \approx \tan 3^{o}$ $x \approx 30^{o}$
	Commented by jagoll last updated on 18/Apr/20

	$thank you sir$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum