Question

Helpp dam naj zad w załączniku trygonometria

Answer 1

Odpowiedź:

5/t = sin60° = √3/2

5 = t * √3/2

t = 5 : √3/2 = 5 * 2/√3 = 10/√3 =10√3/3 [j]

z/t = cos60° = 1/2

z = t  * 1/2 = 10√3/3 * 1/2 = 10√3/6  = 5√3/3 [j]

5/x = sin45° = √2/2

5 = x * √2/2

x = 5 : √2/2 = 5 * 2√2 = 10/√2 = 10√2/2 = 5√2 [j]

y/x = cos45° = √2/2

y = x * √2/2 = 5√2 * √2/2  = 5 * 2/2 = 5 [j]

o - obwód = x + y + z + t = 5√2 + 5 + 5√3/3 + 10√3/3 =

= 5√2 + 15√3/3 + 5 = 5√2 + 5√3 + 5 = 5(√2 + √3 + 1) [j]

P - pole trójkąta = 1/2 *(z + y) * 5 = 1/2 * (5√3/3 + 5) * 5 =

= (5√3/6 + 5/2) * 5 = 25√3/6 + 25/2 = (25√3/6 + 75/6) =

= (25√3+ 75)/6  = 25(√3 +3)/6 = 4,1(6) * (√3 + 3) [j²]

[j] - znaczy włąściwa jednostka