How do you find the exact value of the third side given triangle ABC, b=12.4, c=8.70, mangleA23?

Feb 24, 2018

Third side color(purple)(a = 5.55 color(purple)(units

Explanation:

Given : $b = 12.4 , c = 8.7 , \hat{A} = {23}^{\circ}$

To find color(red)(a

Applying Law of cosines,

${a}^{2} = {b}^{2} + {c}^{2} - 2 b c \sin A$

${a}^{2} = {12.4}^{2} + {8.7}^{2} - \left(2 \cdot 12.4 \cdot 8.7 \cdot \cos 23\right)$

${a}^{2} = 30.8419$

a = sqrt 30.8419 = color(purple)(5.55 color(purple)(units