Increases

 I heard a news report that there were 111 deaths among the homeless due to Covid. This was a 23% increase. Sad news of course, but it made me think of what that meant if you wanted to know what the amount was previously. A little algebra would do the trick.

Assume there were "x" deaths previously, so the equation would be:

                        x deaths plus a 23% increase is 111

                        x + 0.23x = 111        

                         1.23x = 111

                         x = 111/1.23

                         x = 90

A practical, every day application

Measuring Mountains

Here is an interesting item I saw online

"Accurately measuring miniscule changes in a mountain that is more than 5 miles us is no easy feat, but surprisingly, measurements rely on geometric formulas and surveying techniques that haven't changed all that much since the 1800's, said Peter Molnar, a geologist at the university of Colorado, Boulder.

At heart, measuring a mountain relies on basic ninth-grade math. To calculate the elevation of a mountain, scientists would measure the distance. between two points on the ground and then measure the angles between the top of the mountain and each point. 

"if you have two angles, you know the third, because the sum of the angles is 180 [degrees], Molnar told Live Science. 

To carry out these measurements, surveyors must identify a horizontal surface using a level (which, like the kind at a hardware store, relies on a trapped air bubble that, under the influence of gravity, slides closer to or farther away from a central region as it tilts". From there, surveyors eye the summit and measure the angle with the assistance of a glorified highly accurate protractor - a telescopic device known as a theodolite. With two angles and one side of  a triangle, trigonometry reveals the lengths of the other sides, and thereby, the height of the triangle (the mountain)."

If I'm getting the picture they are trying to convey, this method (I assume the Law of Sines) would not give the height. It would give distances from each of the individuals to the top of the mountain. .From there, you could use one of those distances and set up a vertical right triangle and measure the angle of elevation to the summit. Then you could simply use: Sin(measure of angle of elevation) = opposite side / hypotenuse. Solve the equation for  the opposite side and that is the height of the mountain.

There were other interesting things in the article. That can be for another time.