Question

a) 0,73
b)0,81
c)0,97
d)1,01
e)1,72​

Answer 1

Lei dos Cossenos

${a}^{2} = {b}^{2} + {c}^{2} - 2.b.c.\cos \alpha$

Daí,

${8}^{2} = {5}^{2} + {7}^{2} - 2.5.7.cosx \\ \\ cosx = \frac{64 - 25 - 49}{ - 70} = \frac{ - 10}{ - 70} = \frac{1}{ 7}$

Da relação, temos

${sen}^{2} x + {cos}^{2} x = 1$

$com \: 0 < x < 180°$

${sen}^{2} x = 1 - {cos}^{2} x \\ \\ = 1 - {( \frac{1}{7} )}^{2} = 1 - \frac{1}{49} \\ \\ = \frac{48}{49} \\ \\ senx = \sqrt{ \frac{48}{49} } = \frac{ \sqrt{48} }{7} = \frac{4 \sqrt{ 3}}{7} \\ \\ senx = \frac{4.1,7}{7} = 0,97$