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User Staticsan
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We have 3 triangles that are related in the image

We will use the sine relations to determine the value of x

For triangle ABD


\begin{gathered} (24)/(\sin d)=(16)/(\sin b)=(2x+4+2x)/(\sin a) \\ \\ (24)/(\sin d)=(16)/(\sin b)=(4x+4)/(\sin a) \\ \\ \end{gathered}

For triangle ABC


(24)/(\sin c1)=(E)/(\sin b)=(2x+4)/(\sin a1)

For triangle ACD


(16)/(\sin c2)=(E)/(\sin d)=(2x)/(\sin a2)

Now solving the system of equations we have


\begin{gathered} 4x+4=20 \\ 4x=20-4 \\ 4x=6 \\ x=4 \end{gathered}

The answer would be x = 4 units

Could you help with-example-1
Could you help with-example-2
User Stvn
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