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Question Number 83369 by Power last updated on 01/Mar/20

Commented by mr W last updated on 01/Mar/20

$$\mathrm{\angle }A=90°$$$$\Rightarrow AD=BD=DC=5$$

Commented by mathmax by abdo last updated on 01/Mar/20

$$weusetheformulae{AB}^2+{AC}^2=2{AD}^2+\frac{{BC}^2}{2}\Rightarrow$$$$8^2+6^2=2{AD}^2+\frac{{100}^2}{2}\Rightarrow 2{AD}^2=100-50=50\Rightarrow {AD}^2=25\Rightarrow$$$$AD=5$$

Answered by mind is power last updated on 01/Mar/20

$$cos\left(B\right)=\frac{{10}^2+8^2-6^2}{2.10.8}=\frac{128}{160}=\frac{4}{5}$$$${AD}^2=8^2+5^2-2.8.5cos\left(B\right)=64+25-64=25$$$$AD=5$$

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