Вправи: 604

604. Розв’яжіть трикутник, якщо:

1) якщо a – b = 5, ∠A = 54°, ∠B = 13°, то a = 5 + b,

то asinA = bsinB, 5+ bsin∠A = bsin∠B;

(5 + b)sin∠B = b sin∠A, 5sin∠B = bsin∠A – bsin∠B, b(sin∠A – sin∠B) = = 5sin∠B, b = 5sin∠Bsin∠A- sin∠B, b = 5sin13°sin54°- sin13°, b ≈ 5•0,2250,809-0,225 =

= 1,1250,584 ≈ 1,9, a ≈ 5 + 1,9 = 6,9: ∠C = 180° – (54° + 13°) = 113°;

csin113° = bsin∠B, c = bsin113°sin∠B, c ≈ 1,9sin113°sin13° ≈ 1,9•0,92050,225 ≈ 7,8.

Відповідь: b ≈ 1,9; a ≈ 6,9; c ≈ 7,8; ∠C = 113°.

2) якщо b + c = 7, ∠A = 29°, ∠B = 47°, то ∠C = 180° – (29° + 47°) =

= 104°; b = 7 – c і bsin∠B = csin∠C, 7- csin47° = csin104°;

(7 – c)sin104° = csin47°, 7sin104° = csin47° + csin104°, c(sin47° +

+ sin104°) = 7sin104°, c = 7sin104°sin47°+ sin104°, c = 7•0,97030,7314+0,9603 =

= 6,79211,7017 ≈ 4; b = 7 – 4 = 3; asin∠A = bsin∠B, a = bsin∠Asin∠B,

a ≈ 3• sin29°sin47° ≈ 3•0,48480,7314 ≈ 2.

Відповідь: ∠C = 104°; c ≈ 4; b ≈ 3; a ≈ 2.