WPP #12 Unit O Concept 10: Elevation and Depression

         1.)  Hannah realizes that she wants to glide down a building into a soft bush. She climbs a 500 ft building, reaches the top, and gazes down at the bush at an angle of 25 degrees 10'. If Hannah was to glide perfectly horizontally, then suddenly fall onto the bush, what would be the distance she traveled horizontally.

THE PROBLEM

In order to solve this problem, first we need to calculate the value of 25 degrees 10'. We accomplish this by placing 10 over 60 (because there are 60 seconds in a minute) to get 10/60 which simplifies to 1/6 which, in decimal form, is .17. After we get the angle value, we can utilize trig functions. In the below picture, I use tan.  Tan is y/x so we use 500/x. We don't want variables as the denominator so we multiply both sides by x. We have to get x by itself so we divide both sides by tan 25.17. Our answer is 1063.99 which rounds to 1064 ft.

                                                                       The Solution

          2.) Hannah, after landing on the bush, has just discovered that she is terrified of falling. She deduces that what she loves is parkour. She loves to jump from buildings to buildings. She climbs the same building as the last problem, but wants to jump to the top of a 1000 ft building. She looks at the top of that building at an angle of 32 degrees 6' and reassures herself that she is the queen of pop. There is no way that she can fail this measly task of jumping 500 feet. How far is the building she is currently on from the building she wants to jump to?

THE PROBLEM

 To solve this problem, we must again find the angle value. We take 6 and divide it by 60 to get 1/10 which is essentially .1 which we add to 32 of course. To find our opposite side, just take the side value of the big building and subtract it by the height of the smaller building. Once we have found that out, we can use a trig function. I am a fan of tan, so I used tan once again. It is the same old song and dance as we multiply both sides by x and then divide by tan 32.1 to get our answer of 797.068 which is simplified to 797.07 feet.

THE SOLUTION