7. Mekkora annak a rombusznak a szögei, melynek átlói 12 cm és 16 cm hosszúak?

`AB = \sqrt{AO^2 +BO^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10`

`AO = \frac{AC}{2} = \frac{12}{2} = 6 cm`
`BO = \frac{BD}{2} = \frac{16}{2} = 8 cm`

`\frac{AB}{AO} = \frac{sin \hat{AOB}}{sin \hat{ABO}} " " => " " \hat{ABO} = arcsin \frac{AO * sin \hat{AOB}}{AB} = arcsin \frac{6 * sin 90}{10} = arcsin \frac{6 * 1}{10} = arcsin .6 = 36.869898^\circ`

`\frac{AB}{BO} = \frac{sin \hat{AOB}}{sin \hat{BAO}} " " => " " \hat{BAO} = arcsin \frac{BO * sin \hat{AOB}}{AB} = arcsin \frac{8 * sin 90}{10} = arcsin \frac{8 * 1}{10} = arcsin .8 = 53.130102^\circ`

`\hat{ABC} = \hat{ABO} * 2 = 36.869898 * 2 = \color{red}73.739795^\circ`
`\hat{BAD} = \hat{BAO} * 2 = 53.130102 * 2 = \color{red}106.260205^\circ`