Question Number 9677 by ridwan balatif last updated on 23/Dec/16
Commented by geovane10math last updated on 23/Dec/16
$${An}\:{acute}\:{angle}\:{can}\:{not}\:{measure}\:\mathrm{129}° \\ $$$$\mathrm{51}°\:+\:\mathrm{78}°\:=\:\mathrm{129}° \\ $$
Commented by ridwan balatif last updated on 24/Dec/16
$$\mathrm{ooh}\:\mathrm{i}'\mathrm{m}\:\mathrm{so}\:\mathrm{sorry},\:\mathrm{i}'\mathrm{m}\:\mathrm{forget}\:\mathrm{to}\:\mathrm{say}\:\mathrm{that}\:\mathrm{point}\: \\ $$$$\mathrm{D}\:\mathrm{is}\:\mathrm{in}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{of}\:\mathrm{line}\:\mathrm{BC} \\ $$
Answered by mrW last updated on 23/Dec/16
$$\alpha=\mathrm{78}° \\ $$$$\beta=\mathrm{51}° \\ $$$$\mathrm{a}=\mathrm{AC}=\mathrm{12}\:\mathrm{cm} \\ $$$$\mathrm{L}=\mathrm{AD} \\ $$$$\frac{\mathrm{L}×\mathrm{sin}\:\beta}{\mathrm{a}×\mathrm{sin}\:\left(\alpha+\beta\right)}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{L}=\frac{\mathrm{sin}\:\left(\alpha+\beta\right)×\mathrm{a}}{\mathrm{2sin}\:\beta}=\frac{\mathrm{sin}\:\left(\mathrm{129}°\right)×\mathrm{12}}{\mathrm{2sin}\:\mathrm{51}°}=\mathrm{6}\:\mathrm{cm} \\ $$