Here is Cara. She was walking through her local park when she heard meows from a tree. She was quite shocked. The cat was 32 feet above ground! She stood 9 feet away from the cat. At what angle must she place the ladder so she can reach the cat from where she was stood? How long of a ladder must she need?
Luckily, she still remembered some geometry and figured out that to find the angle that she must place the ladder, she will need to solve with the formula tanø=0/a, and in this instance, it would translate to tan-1(x)=32/9. To solve for x, she must find the inverse tangent (32/9)=x. Cara must place the ladder at about 74.3 degrees.
As the day draws to a close, Cara must hurry up, as just the angle won't do her any good without a ladder. Now, she only needs to find the length of the ladder that she must use. For this, she used the formula sinø=0/h, which in this case, Cara solved the equation
sin(74.3)=32/y. Multiply by y on both sides. divide by the sin of 74.3 on both sides, and the length of the ladder has to be approximately 33.2 feet long to be able to reach the cat from where she was standing. Luckily she didn't have to call the firefighters for this one.
Now that she had brought the cat home, Cara faced another problem: she didn't have any cat supplies1 Luckily her neighbor had some cat food to give temporarily, but her new best friend didnt't have anything to play with. Eventually, she settled on a plan to install a shelf so the cat could jump on it and look out the window.
She knew that the distance from her eye level to the shelf was 5 feet, and that she was looking up at a 25 degree angle. She also stood 3 feet away from where her table would be. How high up must she place the shelf from her eye level?
to lounge on.
With this information, she found the angle measure of the third angle in the triangle to be 65 degrees. Now, to find x, she used the formula cosø=a/h, and when solved for x, it would be h*cosø=a. So, x=5*cos(65), which results to x=2.1 feet. With her newfound information, Cara went straight to work on installing a shelf for her cat
At the end of today, Cara was grateful to have found a new best friend, and I am sure that the cat also feels lucky to have found someone to love him. It was a happy ending.