Summarize the following:
To find the missing angle of a triangle using the cosine rule, you need to know the length of all three sides of the triangle. For example, you might have triangle RST. Side SR is 8 cm long. Side ST is 10 cm long. Side RT is 12 cm long. What is the measurement of angle S? The formula is c2=a2+b2−2abcos⁡C{\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos {C}}. In this formula, cos⁡C{\displaystyle \cos {C}} equals the cosine of the angle you are trying to find. The variable c{\displaystyle c} equals the side opposite the missing angle. The variables a{\displaystyle a} and b{\displaystyle b} are the lengths of the other two sides. Plug these values into the formula. For example, since side RT is opposite the missing angle, angle S, side RT will equal c{\displaystyle c} in the formula. The other two side lengths will be a{\displaystyle a} and b{\displaystyle b}. It doesn’t matter which side is which variable. So, your formula should look like this: 122=82+102−2(8)(10)cos⁡C{\displaystyle 12^{2}=8^{2}+10^{2}-2(8)(10)\cos {C}}. You are multiplying 2ab{\displaystyle 2ab} times the cosine of the missing angle, which you don’t know yet. So, the variable should remain. For example, 122=82+102−160cos⁡C{\displaystyle 12^{2}=8^{2}+10^{2}-160\cos {C}}. Remember that to square a number, you multiply the number by itself. For example, 144=82+102−160cos⁡C{\displaystyle 144=8^{2}+10^{2}-160\cos {C}} Make sure you square each number first, and then add them together. For example:144=64+100−160cos⁡C{\displaystyle 144=64+100-160\cos {C}}144=164−160cos⁡C{\displaystyle 144=164-160\cos {C}} To do this, subtract the sum of a2{\displaystyle a^{2}} and b2{\displaystyle b^{2}} from both sides of the equation. Then, divide each side of the equation by the coefficient of the missing angle’s cosine. For example, to isolate the cosine of the missing angle, subtract 164 from both sides of the equation, then divide each side by -160:144−164=164−164−160cos⁡C{\displaystyle 144-164=164-164-160\cos {C}}−20=−160cos⁡C{\displaystyle -20=-160\cos {C}}−20−160=−160cos⁡C−160{\displaystyle {\frac {-20}{-160}}={\frac {-160\cos {C}}{-160}}}0.125=cos⁡C{\displaystyle 0.125=\cos {C}} This will give you the measurement of the missing angle. On a calculator, the inverse cosine key is denoted by COS−1{\displaystyle COS^{-1}}. For example, the inverse cosine of .0125 is 82.8192. So, the missing angle, angle S, is 82.8192 degrees.

summary: Assess what values you know. Set up the formula for the Cosine Rule. Determine the values of a{\displaystyle a}, b{\displaystyle b}, and c{\displaystyle c}. Complete the necessary multiplication. Find the square of c{\displaystyle c}. Add the squares of a{\displaystyle a} and b{\displaystyle b}. Isolate the cosine of the missing angle. Find the inverse cosine.


Summarize the following:
Games that kids won't need much help with (like Candy Land) are best if you are trying to occupy your kids so you can get things done around the house. Try not to use difficult games like Monopoly, unless there is an older child who can help the younger ones.  Card games are good, too. You can find specialty card games for kids, or you can teach your kids to play simple card games like War and Go Fish with a standard deck of cards. If you don’t have any games on hand, teach them to play a game that doesn’t require any materials, such as I Spy, Simon Says, or Red Light, Green Light. You can find puzzles for all different ages and difficulty levels. You can also have children create their own puzzles with cardboard or construction paper, and if you have multiple children, you can ask them to complete each other’s puzzles. This could be playing football, skipping, playing on a trampoline, or playing games with each other such as chase or hide and seek.  If you have smaller children, fill a large bucket or something quite big with water and add plastic boats, rubber ducks and other toys. You can also use this same bucket to put sand in and let them build miniature sand castles. Give them some sports equipment and tell them to make up a new sport. You can get creative with the materials by using buckets for targets or trash can lids for bases, for example. You can either hide items around the house, or just create a list of items they will be likely to encounter in the area where you’re playing. You can use furniture or any other household items as obstacles, and set up your course either indoors or outdoors. Make up new rules for each round or rearrange obstacles to keep things interesting. For younger children, encourage critical thinking by making up your own games with materials you already have around the house. You can write numbers or letters on scraps of paper and ask them to put them in the proper order, or give them pictures cut out from magazines and ask them to group them in a specific way. The possibilities are endless.

summary: Give them some board games. Challenge them with a jigsaw puzzle. Let them play outside. Try a scavenger hunt. Set up an obstacle course. Make your own matching games.


Summarize the following:
Mix ¾ cup baking soda, ¼ cup hydrogen peroxide, and 1 tablespoon dish soap. This highly effective paste cleans the grout in three ways:  The baking soda works as a natural abrasive to scrub the grout. The hydrogen peroxide chemically reacts with the baking soda releasing bleaching oxygen ions. The dish soap helps loosen dirt and remove grease. NOTE: The bleaching action of the chemical reaction may affect colored grout. Test a hidden corner before cleaning the entire floor. A toothbrush or a nylon scrub brush work well. Be sure to apply the paste to the grout between all tiles and around the edges for a uniform clean look. You may see a bubbling reaction as the baking soda and hydrogen peroxide interact. Give the paste time to work its way into the grout to fully remove any stains. Pour a small amount of water directly onto the tile floor to rinse the solution off the grout. Use caution as wet tiled floors can be very slippery. Clean the remaining paste out of the grout by gently scrubbing the floor with a towel. This can be done by standing on a towel and shuffling the towel across the floor with both feet or by crawling and scrubbing as you go. Ensure that no soap or residue is left behind by thoroughly mopping the floor with a cotton or sponge mop. Rinse the mop and change the water often to get achieve a clean finish.
summary: Make a paste. Apply the paste with a nylon bristled brush. Let the mixture sit on the grout for 15 minutes. Rinse the grout with warm or hot water to remove all of the solution. Use a rag to wipe the grout to remove any leftover residue or dirt. Mop the floor with clean water.