Month: December 2018

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General Right Triangle Word Problems

Howard is designing a chair swing ride. The swing ropes are 44 meters long, and in full swing, they tilt in an angle of 23°. Howard wants the chairs to be 3.5 meters above the ground in full swing.
 
How tall should the pole of the swing ride be?
Round your final answer to the nearest hundredth.
 
 
In order to do this problem, we have to apply the law of sines.
 
sin (67°) / x = sin (90°) / 4
x = 3.68
 
Where does 67° come from?
      If we draw a line perpendicular to the pole to the hypotenuse, we got a 90° angle. So, 180°- (90° + 23°) = 67°. 
 
We haven’t finished yet, we need to add x to 3.5 because they ask the entire length of the pole. 
3.68 m + 3.5 m = 7.18 m
 
*It is better to not round your answer during your calculation*
 
How tall should the pole of the swing ride be?
Round your final answer to the nearest hundredth.
 
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VSEPR Model

Valence

Shell

Electron

Pair

Repulsion

VSEPR is a model used in Chemistry in order to predict a geometric shape of molecules based on the number of valence electrons. 

We can classify molecules into 7 main geometric shapes:

  • Linear                                      180°                    Non-Polar
  • Bent                                         104.5°                Polar
  • Trigonal Planar                   120°                    Non-Polar
  • Trigonal Pyramidal           107.3°                Polar
  • Tetrahedral                          109.5°                Non-Polar
  • Trigonal Bipyramidal       90°/ 120°         Non-Polar
  • Octahedral                           90°                      Non-Polar

Before figuring out any of those shapes, we need to draw Lewis Dot Diagram first. Let’s look at some examples:

 

Based on its Lewis Dot structure, we can classify HCN as Linear. 

As you can see above, Sulfur has 5 bonds. So, we would classify this as Trigonal Bipyramidal. 

Now, in this case, Sulfur has only 2 bonds. We would classify this as Bent. Why? HCN also has only 2 bonds but classified as Linear. That is because there are two extra pairs of electrons in the middle atom so those two pairs of electrons will push each of the two bonds down, creating an angle.