This document contains solutions to geometry problems. It solves for variables like x, r, and d in different equations related to circles, triangles, and trigonometry. Key details calculated include x=9 cm, r≈76.43 cm, and d=250 cm.

1. 5.
Gabarito:
1.
(
C= d
π
)
2
(
x
2
+6 3
x
2
+
108 =432
= 12 3
x 2 =432 −
108
x
2
=324
x = 324
)
2
6 3
sen β =
12 3
1
sen β =
2
β =30º
2.
(
)
2
x
2
x
= −27
36
x
2
=6 2
+27 =36
2
=
9
x= 9
x =3 cm
3 3
3
sen α=
=
6
2
3 1
cos α= =
6 2
3 3
tg α=
= 3
3
sen β =cos α=
1
2
cos β = sen α =
3
2
3
1
3
3
tg β =
=
⋅
=
3
3 3
3
3
3.
C = ⋅60
8
C=
480cm
C= π
2 r
480 = ⋅3,14 ⋅r
2
480
=
r
6,28
r ≅ ,43 cm
76
4.
10,6
tg 32º =
x
10,6
0,63 =
x
10,6
x=
0,63
x = ,83 cm
16
(d )
π
d=
250 cm
(e )
x = cm
18
x2 +3 3
250 π= ⋅d
π
250 π
=
d