Question

Determine o valor de X nos respectivos triangulos.

Answer 1

a) use lei dos senos.

$\frac{x}{ \sin(30) } = \frac{12}{ \sin(45) } \\ \frac{x}{ \frac{1}{2} } = \frac{12}{ \frac{ \sqrt{2} }{2} }$

$\frac{ \sqrt{2} }{2} x = \frac{1}{2} .12 \\ x = \frac{12}{ \sqrt{2} } \\ x = \frac{ 12\sqrt{2} }{2} = 6 \sqrt{2}$

b) use lei dos cossenos.

${x}^{2} = {10}^{2} + {16}^{2} - 2.10.16. \cos(60)$

${x}^{2} = 100 + 256 - 2.160. \frac{1}{2} \\ {x}^{2} = 356 - 160 \\ {x}^{2} = 196 \\ x = \sqrt{196}$

$x = 14$