# Trianlge ABC has AB=33, AC=88, BC=77. Point D lies on BC with BD=21. Compute angle BAD.

Angle bisector theorem for computing an angle
Trianlge ABC has $AB=33,AC=88,BC=77.$. Point D lies on BC with $BD=21.$. Compute $\mathrm{\angle }BAD.$.
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Teagan Zamora
Step 1
Its simple arithmetic:
${77}^{2}={33}^{2}+{88}^{2}-2\left(33\right)\left(88\right)cos\left(\mathrm{\angle }BAC\right)$.
Here you can see every term has a factor of ${11}^{2}$.
$\left({11}^{2}\right){7}^{2}={3}^{2}\left(11{\right)}^{2}+{8}^{2}\left(11{\right)}^{2}-\left({11}^{2}\right)2\left(3\right)\left(8\right)cos\left(\mathrm{\angle }BAC\right)$
Step 2
You can cancel out this factor by dividing by ${11}^{2}$ on both sides.
${7}^{2}={3}^{2}+{8}^{2}-2\left(3\right)\left(8\right)cos\left(\mathrm{\angle }BAC\right)$