Doplňte velikost chybějícího úhlu a
určete, je-li daný trojúhelník ostroúhlý(O), pravoúhlý(P)
nebo tupoúhlý(T) a rovnostranný (RS), rovnoramenný (RR) nebo obecný (O).
|
α |
β |
γ |
* |
* |
|
60˚ |
30˚ |
˚ |
O – P – T |
RS – RR – O |
|
50˚ |
˚ |
25˚ |
O – P – T |
RS – RR – O |
|
˚ |
45˚ |
90˚ |
O – P – T |
RS – RR – O |
|
60˚ |
˚ |
60˚ |
O – P – T |
RS – RR – O |
|
40˚ |
70˚ |
˚ |
O – P – T |
RS – RR – O |
|
47˚ |
˚ |
36˚ |
O – P – T |
RS – RR – O |
|
133˚ |
39˚ |
˚ |
O – P – T |
RS – RR – O |
|
˚ |
47˚ |
86˚ |
O – P – T |
RS – RR – O |
|
˚ |
27˚ |
95˚ |
O – P – T |
RS – RR – O |
|
57˚ |
˚ |
89˚ |
O – P – T |
RS – RR – O |
Určete, zda lze (L) nebo nelze (N)
sestrojit trojúhelník s uvedenými délkami stran. Pokud sestavit lze,
určete obvod a jestli se jedná o trojúhelník rovnostranný (RS), rovnoramenný
(RR) nebo obecný (O).
|
a |
b |
c |
* |
* |
* |
|
5 cm |
5 cm |
5 cm
|
L - N |
o = |
RS – RR – O |
|
1 cm |
2 cm |
4 cm
|
L - N |
o = |
RS – RR – O |
|
10 cm |
7 cm |
9 cm
|
L - N |
o = |
RS – RR – O |
|
3 cm |
8 cm |
3 cm
|
L - N |
o = |
RS – RR – O |
|
6 cm |
3 cm |
3 cm
|
L - N |
o = |
RS – RR – O |
|
5 cm |
4 cm |
3 cm
|
L - N |
o = |
RS – RR – O |
|
12 cm |
13 cm |
5 cm
|
L - N |
o = |
RS – RR – O |
|
1 cm |
10 cm |
1 cm
|
L - N |
o = |
RS – RR – O |
|
11 cm |
6 cm |
6 cm
|
L - N |
o = |
RS – RR – O |
|
7 cm |
7 cm |
4 cm
|
L - N |
o = |
RS – RR – O |
Určete obsah těchto trojúhelníků:
1)
a = 10 cm, va = 6
cm
2)
b = 7 cm, vb = 5
cm
3)
c = 4 cm, vc
= 3 cm
4)
a = 18 cm, va =
10 cm
5)
b = 40 cm, vb =
24 cm
6)
c = 12 cm, vc = 8
cm
7)
ǀABǀ = 8 cm, vc = 7 cm
8)
ǀBCǀ = 9 cm, va = 5 cm
9)
ǀACǀ = 11 cm, vb = 8 cm
10)
ǀACǀ = 13 cm, ǀABǀ
= 10 cm vb = 8 cm
11)
a
= 21 cm, b = 17 cm, vb = 13 cm
12)
b
= 14 cm, vb
= 10 cm, vc = 8 cm
13)
vb = 6 cm, vc = 10 cm, b
= 11 cm
14)
ǀACǀ = 8 cm, vc = 7 cm, ǀABǀ = 10 cm
15)
ǀABǀ = 16 cm, vb =9
cm,
vc = 13 cm
16)
a = 3 cm, b = 4 cm, c = 5 cm
17)
a = 8 cm, b = 10 cm, c = 10 cm
18)
a = 10 cm, b = 12 cm, c = 15 cm
19)
a = 20 cm, b = 41 cm, c =42 cm
20)
a = 9 cm, b = 41 cm, c = 4 dm
Výsledky:
|
90 |
P |
O |
L |
15 cm |
RS |
1) 30 cm2 |
11) 110,5 cm2 |
|
105 |
T |
O |
N |
- |
- |
2) 17,5 cm2 |
12) 70 cm2 |
|
45 |
P |
RR |
L |
26 cm |
O |
3) 6 cm2 |
13) 33 cm2 |
|
60 |
O |
RS |
N |
- |
- |
4) 90 cm2 |
14) 35 cm2 |
|
70 |
O |
RR |
N |
- |
- |
5) 480 cm2 |
15) 104 cm2 |
|
97 |
T |
O |
L |
12 cm |
O |
6) 48 cm2 |
16) 6 cm2 |
|
8 |
T |
O |
L |
30 cm |
O |
7) 28 cm2 |
17) 36,7 cm2 |
|
47 |
O |
RR |
N |
- |
- |
8) 22,5 cm2 |
18) 59,8 cm2 |
|
58 |
T |
O |
L |
23 cm |
RR |
9) 44 cm2 |
19) 402,3 cm2 |
|
34 |
O |
O |
L |
18 cm |
RR |
10) 52 cm2 |
20) 180 cm2 |