Quick Answer SSS
Proof
AC = DB
AB = DC
BC = BC This side is equal to itself and is common to both triangles.
Three sides of one triangle equal to 3 sides of the other means that the triangles are congruent. It is the Theorem you need.
Numerator
<span><span>cos<span>(<span>π/2</span>−x)</span></span>=<span>cos<span>(<span>π/2</span>)</span></span><span>cosx</span>+<span>sin<span>(<span>π/2</span>)</span></span><span>sinx</span></span>
now <span><span>cos<span>(<span>π/2</span>)</span></span>=0 and <span>sin<span>(<span>π/2</span>)</span></span>=1</span>
simplifies to : 0 + sinx = sinx
Denominator
<span><span>sin<span>(<span>π/2</span>−x)</span></span>=<span>sin<span>(<span>π/2</span>)</span></span><span>cosx</span>+<span>cos<span>(<span>π/2</span>)</span></span><span>sinx</span></span>
simplifies to : cosx + 0 = cosx
<span>⇒<span><span>cos<span>(<span>π/2</span>−x)</span></span><span>sin<span>(<span>π/2</span>−x)</span></span></span>=<span><span>sinx/</span><span>cosx</span></span>=<span>tan<span>x</span></span></span>
We are given
P = $754.43
r = 13.6% annual
for a.
A = 150
for b.
A = 300
First, change the interest into effective monthly
i = (1 + 0.136/12)^12 - 1
Solve for i
Next, use the general formula
A = P i ( 1 + i)^n / (1 + 1)^n - 1
Subsitute P, i, and A for a and b.
Then, solve for n for a and b.
