I am not sure about all of them, but it says to write the answers in simplest form, but number 4 is not in simplest form.
4/12 can be simplified to 1/3
By doing so, they provide the illusion that the payments are cheaper then 1000 dollars, because 50 looks very small, when in reality it's $100 more then what the mattress is actually worth.
Answer:
![tan(A) = \frac{3}{4}](https://tex.z-dn.net/?f=tan%28A%29%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
Given
Right-angled triangle ABC
![b = 8](https://tex.z-dn.net/?f=b%20%3D%208)
Required
Calculated tan(A)
First, we calculate the length of a.
Since the triangle is right-angled at C, then c is the hypotenuse and side a is the opposite of A.
So, we have:
![c^2 = a^2 + b^2](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2)
![10^2 = a^2 + 8^2](https://tex.z-dn.net/?f=10%5E2%20%3D%20a%5E2%20%2B%208%5E2)
![100 = a^2 + 64](https://tex.z-dn.net/?f=100%20%3D%20a%5E2%20%2B%2064)
![a^2 = 100 - 64](https://tex.z-dn.net/?f=a%5E2%20%3D%20100%20-%2064)
![a^2 = 36](https://tex.z-dn.net/?f=a%5E2%20%3D%2036)
Take square roots
![a = 6](https://tex.z-dn.net/?f=a%20%3D%206)
So:
![tan(A) = \frac{a}{b}](https://tex.z-dn.net/?f=tan%28A%29%20%3D%20%5Cfrac%7Ba%7D%7Bb%7D)
![tan(A) = \frac{6}{8}](https://tex.z-dn.net/?f=tan%28A%29%20%3D%20%5Cfrac%7B6%7D%7B8%7D)
![tan(A) = \frac{3}{4}](https://tex.z-dn.net/?f=tan%28A%29%20%3D%20%5Cfrac%7B3%7D%7B4%7D)