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# help geometry

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In quadrilateral ABCD, it is given that $$\angle A = 120^{\circ}$$, angles B and D are right angles, AB = 13, and AD = 46. Then what is AC?

Mar 19, 2022

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What is AC?

Hello Guest!

Point A is the origin of an x-y coordinate system.

$$f(x)=-tan(\ 60^\circ)\cdot x\\ x_D=-46\cdot cos(\ 60^\circ)=-23\\ y_D=46\cdot sin(\ 60^\circ)=39.837$$

$$g(x)=tan(\ 30^\circ)\cdot (x+23)+39.837\\ x_C=13\\ g(13)=y_C=tan(\ 30^\circ)\cdot (13+23)+39.837\\ y_C=60.622$$

$$\overline{AC}=\sqrt{13^2+60.622^2}$$

$$\overline{AC}=62$$

!

Mar 20, 2022
edited by asinus  Mar 20, 2022