Question

urgent!! dau coroana!!!! ​

Answer 1

Explicație pas cu pas:

a) ducem CN ⊥ AB

$AC \: bisectoare => ∠DAC = ∠CAB = 45°$

$=> ∠ACN = 45°$

$=> ΔACN \: dreptunghic \: isoscel$

$=> AN = CN$

$AC = 5 \sqrt{2} \: cm => CN = 5 \: cm$

$ΔCNB: NB² = BC² - CN² = 13² - 25² = 169 - 25 = 144$

$=> NB = 12 cm$

$cos(∠NBC) = \frac{NB}{BC} = \frac{12}{13}$

$=> cos(∠ABC) = \frac{12}{13}$

b) M simetric

$=> AC = CM = 5 \sqrt{2} \: cm$

$DC = AN = 5 \: cm$

$∠DCM = 90° + 45° = 135°$

$cos135° = cos(90° + 45°) = - cos45° = - \frac{ \sqrt{2} }{2}$

$ΔDCM: \: DM² = DC² + CM² - 2×DC×CM× cos(∠DCM) \: = {5}^{2} + ({5 \sqrt{2} })^{2} - 2 \times 5 \times 5 \sqrt{2} \times \cos(135) = 25 + 50 - 50 \sqrt{2} \times ( - \frac{ \sqrt{2} }{2}) = 75 + 50 = 125$

$DM = \sqrt{125} = 5 \sqrt{5} \: cm$