Question

In tabelul de mai jos sunt elementele unui triunghi abc ∠a = 90°. Completati tabelul stiind ca dimensiunime segmentelor sunt masurate in centimetri.

B) AB=54 AC=? BC=90 sin b =? sin c=? cos c =? tg b =? tg c =? ctg b = ? ctg c =?

Answer 1

$abc \: a = 90 > {ac}^{2} = {bc}^{2} - {ab}^{2} = {90}^{2} - {54}^{2} = 8100 - 2916 = \sqrt{5184} = 72 \:$

$\sin(b) = \frac{ac}{bc} = \frac{72}{90} = \frac{36}{45}$

$\sin(c) = \frac{ab}{bc} = \frac{54}{90} = \frac{27}{45}$

$\cos(c) = \frac{ac}{ab} = \frac{72}{90} = \frac{36}{45}$

$\tan(b) = \frac{ac}{ab} = \frac{72}{54} = \frac{36}{27}$

$\cot(b) = \frac{ab}{ac} = \frac{54}{72} = \frac{27}{36}$

$\tan(c) = \frac{ac}{ab} = \frac{72}{54} = \frac{36}{27}$