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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

Best Answer 

 #1
avatar+26329 
+15

rectangle

 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:

 Another rectangle

Here again θ = 18.5° but this time we have

$${\mathtt{L}} = {\frac{{\mathtt{8}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)}}} \Rightarrow {\mathtt{L}} = {\mathtt{23.909\: \!479\: \!701\: \!948\: \!374\: \!2}}$$

.

 

 

 

.

Alan  May 8, 2015
Sort: 

2+0 Answers

 #1
avatar+26329 
+15
Best Answer

rectangle

 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:

 Another rectangle

Here again θ = 18.5° but this time we have

$${\mathtt{L}} = {\frac{{\mathtt{8}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{18.5}}^\circ\right)}}} \Rightarrow {\mathtt{L}} = {\mathtt{23.909\: \!479\: \!701\: \!948\: \!374\: \!2}}$$

.

 

 

 

.

Alan  May 8, 2015
 #2
avatar+91045 
0

They are really good sketches Alan :)

Melody  May 9, 2015

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