How do you find remaining sides and angles of triangle given side a =4, side b = 1, angle y = 100?

Feb 26, 2018

Answer:

color(red)(c = 4.2883, hatA = 66.7^@, hat B = 13.3^@

Explanation:

$\hat{C} = {100}^{\circ} , b = 1 , a = 4$

To find $c , \hat{A} , \hat{B}$

Applying law of Cosines,

$c = \sqrt{{a}^{2} + {b}^{2} - \left(2 a b \cos C\right)}$

$c = \sqrt{{4}^{2} + {1}^{2} - \left(2 \cdot 4 \cdot 1 \cdot \cos 100\right)} = 4.2883$

Applying law of sines,

$\hat{A} = {\sin}^{-} 1 \left(\frac{a \sin C}{c}\right) = {\sin}^{-} 1 \left(\frac{4 \cdot \sin 100}{4.2883}\right) = {66.7}^{\circ}$

$\hat{B} = 180 - 100 - 66.7 = {13.3}^{\circ}$