## Trigonometry (11th Edition) Clone

The diagonal opposite the angle of $58^{\circ}$ has a length of 5.2 cm The diagonal opposite the angle of $122^{\circ}$ has a length of 8.8 cm
Let $a = 4.0~cm$, let $b = 6.0~cm$, and let angle $C_1 = 58^{\circ}$. We can use the law of cosines to find $c_1$, the diagonal opposite the angle $C_1$: $c_1^2 = a^2+b^2-2ab~cos~C_1$ $c_1 = \sqrt{a^2+b^2-2ab~cos~C_1}$ $c_1 = \sqrt{(4.0~cm)^2+(6.0~cm)^2-(2)(4.0~cm)(6.0~cm)~cos~58^{\circ}}$ $c_1 = \sqrt{26.56~cm^2}$ $c_1 = 5.2~cm$ Let $a = 4.0~cm$, let $b = 6.0~cm$, and let angle $C_2 = 122^{\circ}$. We can use the law of cosines to find $c_2$, the diagonal opposite the angle $C_2$: $c_2^2 = a^2+b^2-2ab~cos~C_2$ $c_2 = \sqrt{a^2+b^2-2ab~cos~C_2}$ $c_2 = \sqrt{(4.0~cm)^2+(6.0~cm)^2-(2)(4.0~cm)(6.0~cm)~cos~122^{\circ}}$ $c_2 = \sqrt{77.44~cm^2}$ $c_2 = 8.8~cm$