the width of a rectangle is 8 meters. An angle formed by the diagonals is 37. find the length of the rectangle and all the angles in the figure.
+33614 
From symmetry θ = 37°/2 = 18.5°
$${\mathtt{w}} = {\mathtt{8}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)} \Rightarrow {\mathtt{w}} = {\mathtt{2.676\: \!762\: \!556\: \!016}}$$
We are not shown what other angles are needed, but the obvious ones are 90°- θ and 180°-37°
The alternative orientation is:
Here again θ = 18.5° but this time we have
$${\mathtt{L}} = {\frac{{\mathtt{8}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)}}} \Rightarrow {\mathtt{L}} = {\mathtt{23.909\: \!479\: \!701\: \!948\: \!374\: \!2}}$$
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+33614
From symmetry θ = 37°/2 = 18.5°
$${\mathtt{w}} = {\mathtt{8}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)} \Rightarrow {\mathtt{w}} = {\mathtt{2.676\: \!762\: \!556\: \!016}}$$
We are not shown what other angles are needed, but the obvious ones are 90°- θ and 180°-37°
The alternative orientation is:
Here again θ = 18.5° but this time we have
$${\mathtt{L}} = {\frac{{\mathtt{8}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)}}} \Rightarrow {\mathtt{L}} = {\mathtt{23.909\: \!479\: \!701\: \!948\: \!374\: \!2}}$$
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