Free Printable Aplicatii ale trigonometriei in geometrie

1.

In triunghiul ABC se dau $\angle A=45\degree,\ b=\sqrt{2},\ c=1$ .
Atunci latura $a$ a triunghiului are lungimea:

a)

2

b)

3

c)

1

d)

$\sqrt{3-\sqrt{2}}$

e)

$3+\sqrt{6}$

2.

Daca intr-un triunghi ABC raza cercului circumscris este $R=1$ , iar latura $a=1$ , atunci:

a)

$\angle A=30\degree$

b)

$\angle A=120\degree$

c)

$\angle A=45\degree$

d)

$\angle A\in\left\{60\degree,150\degree\right\}$

e)

$\angle A\in\left\{30\degree,150\degree\right\}$

3.

Intr-un triunghi ABC avem $\angle A=90\degree,\ \angle B=15\degree,\ AB=2$ . Atunci latura AC are lungimea :

a)

$2tg\ \frac{\pi}{12}$

b)

$2\operatorname{ctg}15\degree$

c)

$2\sin15\degree$

d)

$2\cos\ \frac{\pi}{6}$

e)

$\frac{2}{\cos15\degree}$

4.

In triunghiul ABC cu $a=\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{2}$ $B=\frac{\pi}{4},\ C=\frac{\pi}{6}$ , raza R a cercului circumscris este data de:

a)

$R=\frac{1}{\sqrt{2}\left(1+\sqrt{3}\right)}$

b)

$R=\frac{1}{1+\sqrt{3}}$

c)

$R=2$

d)

$R=1$

e)

$R=\frac{1+\sqrt{3}}{\sqrt{2}}$

5.

Daca in triunghiul ABC avem $AB=\sqrt{13},\ BC=3,\ \angle C=60\degree$ , atunci:

a)

$AC=4$

b)

$AC=2$

c)

nu exista un asemenea triunghi

d)

$AC=4\sqrt{3}$

e)

$AC=\frac{\sqrt{3}}{2}$

6.

In triunghiul ABC $\sin C=\cos A+\cos B$ . Atunci:

a)

$\Delta ABC$ -echilateral

b)

$\angle A=90\degree$

c)

$\angle B=90\degree$

d)

$\angle A=90\degree\ sau\ \angle B=90\degree$

e)

$\angle A=120\degree$

7.

Fie ABC un triunghi oarecare. Sa se calculeze, in functie de a, b, c, expresia $E=a\left(b\cos C-c\cos B\right)$ .

a)

$E=a\sqrt{b^2+c^2}$

b)

$E=b^2-c^2$

c)

$E=bc$

d)

$E=a\sqrt{bc}$

e)

$E=a^2+b^2+c^2$

8.

Daca intr-un triunghi avem $b=3$ , $c=2,\ B+C=\frac{\pi}{3}$ , atunci $tg\ \frac{B-C}{2}$ este:

a)

$5$

b)

$\frac{5\sqrt{3}}{3}$

c)

$\sqrt{3}$

d)

$\frac{\sqrt{3}}{15}$

e)

$\frac{\sqrt{3}}{5}$

9.

In triunghiul ABC se dau $AB=3,$ $AC=2,\ \angle A=\frac{2\pi}{3}$ . Sa se determine lungimea medianei AM.

a)

$\sqrt{3,5}$

b)

$\sqrt{10}$

c)

$\frac{\sqrt{7}}{2}$

d)

$\frac{\sqrt{19}}{2}$

e)

$\frac{2}{\sqrt{7}}$

10.

Sa se determine unghiul C al triunghiului ABC in care are loc relatia: $\cos A+\cos B=\cos\left(A+B\right)+\frac{3}{2}$ .

a)

$10\degree$

b)

$30\degree$

c)

$45\degree$

d)

$60\degree$

e)

$120\degree$

Aplicatii ale trigonometriei in geometrie

Total questions: 10

Worksheet time: 3hrs 30mins

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