Question

Masura unui unghi si a complementului sau sunt invers proportionale cu 4 si 6. Aflati masura unghului

Answer 1

fie asi b masurile unghiurilor

atunci:

a+b=90

4a=6b

a+b=90

2a=3b

a=3b/2

3b/2+b=90°

5b/2=90°

5b=180°

b=36°

a=3b/2=54 grade

sau a=90-36=54°

Answer 2

$\it x \: + \: y \: = {90}^{o} \\ \it x \cdot 4 = y \cdot 6 = K \: \\ \it x \cdot 4 = K = = > x = \frac{K}{4} \\ \\ \it y \cdot 6 = K = = > y = \frac{K}{6} \\ \\ \it x \: + \: y \: = {90}^{o} = = > \\ \\ \it \: ^{6)} \frac{K}{4} \: + \: ^{4)} \frac{K}{6} \: = \: ^{24)} {90}^{o} = = > \\ \\ \it 6K \: + \: 4K = 2160 = = > \\ \it 10K = 2160 = = > \\ \it K = \frac{2160}{10} = = > \\ \\ \it K = 216 \\ \\ \it x = \frac{K}{4} = \frac{216}{4} = 54^{o} \\ \\ \it y = \frac{K}{6} = \frac{216}{6} = 36 ^{o}$