In a triangle ABC with usual notations,if |ov | vedclass

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(C) Let the sides of the triangle be $a = |\overline{BC}| = 8$,$b = |\overline{CA}| = 7$,and $c = |\overline{AB}| = 10$. We need to find the projectio

Vedclass · Accepted Answer

$\frac{85}{14}$ units

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(C) Let the sides of the triangle be $a = |\overline{BC}| = 8$,$b = |\overline{CA}| = 7$,and $c = |\overline{AB}| = 10$. We need to find the projection of $\overline{AB}$ on $\overline{AC}$. In $	riangle ABC$,by the Law of Cosines,we have $a^2 = b^2 + c^2 - 2bc \cos(A)$. Substituting the values,$8^2 = 7^2 + 10^2 - 2(7)(10) \cos(A)$. $64 = 49 + 100 - 140 \cos(A)$. $64 = 149 - 140 \cos(A)$. $140 \cos(A) = 149 - 64 = 85$. $\cos(A) = \frac{85}{140} = \frac{17}{28}$. The projection of vector $\overline{AB}$ on $\overline{AC}$ is given by $|\overline{AB}| \cos(A)$. Projection $= 10 	imes \frac{17}{28} = \frac{170}{28} = \frac{85}{14}$ units.

In a triangle $ABC$ with usual notations,if $|\overline{BC}|=8, |\overline{CA}|=7, |\overline{AB}|=10$,then the projection of $\overline{AB}$ on $\overline{AC}$ is

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