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# find the length of the rectangle and all the angles in the figure.

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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.

Guest May 8, 2015

#1
+26973
+15

From symmetry θ = 37°/2 = 18.5°

$${\mathtt{w}} = {\mathtt{8}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)} \Rightarrow {\mathtt{w}} = {\mathtt{2.676\: \!762\: \!556\: \!016}}$$

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

$${\mathtt{L}} = {\frac{{\mathtt{8}}}{\underset{\,\,\,\,^{{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)}}} \Rightarrow {\mathtt{L}} = {\mathtt{23.909\: \!479\: \!701\: \!948\: \!374\: \!2}}$$

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Alan  May 8, 2015
#1
+26973
+15

From symmetry θ = 37°/2 = 18.5°

$${\mathtt{w}} = {\mathtt{8}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)} \Rightarrow {\mathtt{w}} = {\mathtt{2.676\: \!762\: \!556\: \!016}}$$

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

$${\mathtt{L}} = {\frac{{\mathtt{8}}}{\underset{\,\,\,\,^{{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)}}} \Rightarrow {\mathtt{L}} = {\mathtt{23.909\: \!479\: \!701\: \!948\: \!374\: \!2}}$$

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Alan  May 8, 2015
#2
+93351
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They are really good sketches Alan :)

Melody  May 9, 2015