Question

Observe o triângulo retângulo e determine o valor dos elementos desconhecidos

Answer 1

Resposta:

X = 60/13 = 4,61

Explicação passo-a-passo:

BH + CH = 13

CH = 13 - BH

5² = BH² + X²

X² = 5² - BH²

12² = CH² + X²

X² = 12² - CH²

X² = X²

5² - BH² = 12² - CH²

25 - BH² = 144 - (13 - BH)²

25 - BH² = 144 - (13² - 2.13.BH + BH²)

25 - BH² = 144 - 169 + 26.BH - BH²

25 - BH² + BH² = 144 - 169 + 26.BH

26.BH = 25 - 144 + 169

26.BH = 50

BH = 50/26 = 1,92

CH = 13 - 50/26 = (338 - 50)/26

CH = 288/26 = 11,08

X² = 5² - (50/26)²

X² = 25 - 50²/26² = (25×26² - 50²)/26²

X² = 14.400/26²

X = √(14.400/26²)

X = 120/26 = 60/13 = 4,61

OU

Sen a = BH/5

Sen a = X/12

BH/5 = X/12

X/BH = 12/5

BH = 5X/12

5² = X² + (5X/12)²

25 = X² + 25X²/144

144×25 = 144X² + 25X²

169X² = 144.25

X² = 144.25/169

X = √(144.25/169)

X = 12.5/13 = 60/13 ≈ 4,61