Odpowiedź:
Zadanie 6
a)
c² = a² + b² a = √3 b = √2
c² = (√3)² + (√2)²
c² = 3 + 2
c² = 5 c = √5
Pole:
P = a*h/2
a = √3; h = √2
P = √3 * √2 / 2
P = √6/2
b)
c² = a² + b² a = 2√3 b = 2
c² = (2√3)² + 2²
c² = 4*3 + 4
c² = 12 + 4
c² = 16
c = √16
c = 4
Pole
a = 2√3 h = 2
P = 2√3 * 2 / 2
P = 4√3 / 2
P = 2√3
c)
c² = a² + b²
a = 5√2 b = 5√2
c² = (5√2)² + (5√2)²
c² = 25*2 + 25*2
c² = 50 + 50
c² = 100
c = √100
c = 10
P = a*h/2 a = 5√2; h = 5√2
P = 5√2 * 5√2 /2
P = 25*2 / 2
P = 50/2
P = 25
3; √5 przeciwprostokątna to 3
c² = a² + b² c = 3 a = √5
(3)² = (√5)² + b²
b² = 9 - 5
b² = 4
b = √4
b = 2
3√5; 4√3 przeciwprostokątna 4√3; a = 3√5
(4√3)² = (3√5)² + b²
b² = (4√3)² - (3√5)²
b² = 16*3 - 9*5
b² = 48 - 45
b² = 3
b = √3
7 ; 4√3 przeciwprostokątna - 7 a = 4√3
7² = (4√3)² + b²
b² = 7² - (4√3)²
b² = 49 - 16*3
b² = 49 - 48
b² = 1
b = √1
b = 1
Zadanie 8
Rozwiązanie w załączniku
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Odpowiedź:
Zadanie 6
a)
c² = a² + b² a = √3 b = √2
c² = (√3)² + (√2)²
c² = 3 + 2
c² = 5 c = √5
Pole:
P = a*h/2
a = √3; h = √2
P = √3 * √2 / 2
P = √6/2
b)
c² = a² + b² a = 2√3 b = 2
c² = (2√3)² + 2²
c² = 4*3 + 4
c² = 12 + 4
c² = 16
c = √16
c = 4
Pole
P = a*h/2
a = 2√3 h = 2
P = 2√3 * 2 / 2
P = 4√3 / 2
P = 2√3
c)
c² = a² + b²
a = 5√2 b = 5√2
c² = (5√2)² + (5√2)²
c² = 25*2 + 25*2
c² = 50 + 50
c² = 100
c = √100
c = 10
Pole
P = a*h/2 a = 5√2; h = 5√2
P = 5√2 * 5√2 /2
P = 25*2 / 2
P = 50/2
P = 25
Zadanie 6
a)
3; √5 przeciwprostokątna to 3
c² = a² + b² c = 3 a = √5
(3)² = (√5)² + b²
b² = 9 - 5
b² = 4
b = √4
b = 2
b)
3√5; 4√3 przeciwprostokątna 4√3; a = 3√5
c² = a² + b²
(4√3)² = (3√5)² + b²
b² = (4√3)² - (3√5)²
b² = 16*3 - 9*5
b² = 48 - 45
b² = 3
b = √3
c)
7 ; 4√3 przeciwprostokątna - 7 a = 4√3
c² = a² + b²
7² = (4√3)² + b²
b² = 7² - (4√3)²
b² = 49 - 16*3
b² = 49 - 48
b² = 1
b = √1
b = 1
Zadanie 8
Rozwiązanie w załączniku