Quick question before I answer: Did he have to pay $2,399 when he signed the lease, or was that just how much he had to pay in total over the course of 36 months?
3% interest on 5,000 = 150
275 (the total amount wanted) - 150 (from initial investment)= 125
x (5%) =125
x (0.05)= 125
x/0.05)= 125/0.05
x=2500
you need to invest 2500 at 5% to get the additional 125
125 plus 150= 275
Step ![1](https://tex.z-dn.net/?f=1)
In the right triangle ADB
<u>Find the length of the segment AB</u>
Applying the Pythagorean Theorem
![AB^{2} =AD^{2}+BD^{2}](https://tex.z-dn.net/?f=AB%5E%7B2%7D%20%3DAD%5E%7B2%7D%2BBD%5E%7B2%7D)
we have
![AD=5\ units\\BD=12\ units](https://tex.z-dn.net/?f=AD%3D5%5C%20units%5C%5CBD%3D12%5C%20units)
substitute the values
![AB^{2}=5^{2}+12^{2}](https://tex.z-dn.net/?f=AB%5E%7B2%7D%3D5%5E%7B2%7D%2B12%5E%7B2%7D)
![AB^{2}=169](https://tex.z-dn.net/?f=AB%5E%7B2%7D%3D169)
![AB=13\ units](https://tex.z-dn.net/?f=AB%3D13%5C%20units)
Step ![2](https://tex.z-dn.net/?f=2)
In the right triangle ADB
<u>Find the cosine of the angle BAD</u>
we know that
![cos(BAD)=\frac{adjacent\ side }{hypotenuse}=\frac{AD}{AB}=\frac{5}{13}](https://tex.z-dn.net/?f=cos%28BAD%29%3D%5Cfrac%7Badjacent%5C%20side%20%7D%7Bhypotenuse%7D%3D%5Cfrac%7BAD%7D%7BAB%7D%3D%5Cfrac%7B5%7D%7B13%7D)
Step ![3](https://tex.z-dn.net/?f=3)
In the right triangle ABC
<u>Find the length of the segment AC</u>
we know that
![cos(BAC)=cos (BAD)=\frac{5}{13}](https://tex.z-dn.net/?f=cos%28BAC%29%3Dcos%20%28BAD%29%3D%5Cfrac%7B5%7D%7B13%7D)
![cos(BAC)=\frac{adjacent\ side }{hypotenuse}=\frac{AB}{AC}](https://tex.z-dn.net/?f=cos%28BAC%29%3D%5Cfrac%7Badjacent%5C%20side%20%7D%7Bhypotenuse%7D%3D%5Cfrac%7BAB%7D%7BAC%7D)
![\frac{5}{13}=\frac{AB}{AC}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B13%7D%3D%5Cfrac%7BAB%7D%7BAC%7D)
![\frac{5}{13}=\frac{13}{AC}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B13%7D%3D%5Cfrac%7B13%7D%7BAC%7D)
solve for AC
![AC=(13*13)/5=33.8\ units](https://tex.z-dn.net/?f=AC%3D%2813%2A13%29%2F5%3D33.8%5C%20units)
Step ![4](https://tex.z-dn.net/?f=4)
<u>Find the length of the segment DC</u>
we know that
![DC=AC-AD](https://tex.z-dn.net/?f=DC%3DAC-AD)
we have
![AC=33.8\ units](https://tex.z-dn.net/?f=AC%3D33.8%5C%20units)
![AD=5\ units](https://tex.z-dn.net/?f=AD%3D5%5C%20units)
substitute the values
![DC=33.8\ units-5\ units](https://tex.z-dn.net/?f=DC%3D33.8%5C%20units-5%5C%20units)
![DC=28.8\ units](https://tex.z-dn.net/?f=DC%3D28.8%5C%20units)
Step ![5](https://tex.z-dn.net/?f=5)
<u>Find the length of the segment BC</u>
In the right triangle BDC
Applying the Pythagorean Theorem
![BC^{2} =BD^{2}+DC^{2}](https://tex.z-dn.net/?f=BC%5E%7B2%7D%20%3DBD%5E%7B2%7D%2BDC%5E%7B2%7D)
we have
![BD=12\ units\\DC=28.8\ units](https://tex.z-dn.net/?f=BD%3D12%5C%20units%5C%5CDC%3D28.8%5C%20units)
substitute the values
![BC^{2}=12^{2}+28.8^{2}](https://tex.z-dn.net/?f=BC%5E%7B2%7D%3D12%5E%7B2%7D%2B28.8%5E%7B2%7D)
![BC^{2}=973.44](https://tex.z-dn.net/?f=BC%5E%7B2%7D%3D973.44)
![BC=31.2\ units](https://tex.z-dn.net/?f=BC%3D31.2%5C%20units)
therefore
<u>the answer is</u>
![BC=31.2\ units](https://tex.z-dn.net/?f=BC%3D31.2%5C%20units)
Worksheet? I need more information on this topic