We are asked to determine the length of sides a, b, and c. First, we will determine the value of "a" using the exterior right triangle shown in the following diagram:
We will use the function tangent since this is defined as:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]
Substituting we get:
[tex]\tan 15=\frac{a}{1}[/tex]
Solving the operations:
[tex]a=\tan 15\approx0.28[/tex]
Now, we will determine the value of "b" using the larger triangle, as shown next:
We will use tangent:
[tex]\tan 15=\frac{1}{b+a+a+a+a}[/tex]
Adding like terms:
[tex]\tan 15=\frac{1}{b+4a}[/tex]
Now, we solve for "b". To do that, we will invert both sides:
[tex]\frac{1}{\tan 15}=b+4a[/tex]
Now, we subtract "4a" from both sides:
[tex]\frac{1}{\tan 15}-4a=b[/tex]
Now, we substitute the value of "a":
[tex]\frac{1}{\tan15}-4\tan 15=b[/tex]
Solving the operations:
[tex]2.66=b[/tex]
Therefore, the value of "b" is 2.66.
Now, we determine the value of "c". To do that we use the following triangle:
Now, we use tangent:
[tex]\tan 15=\frac{c}{b}[/tex]
We multiply both sides by "b":
[tex]b\tan 15=c[/tex]
Substituting the values:
[tex]2.66\tan 15=c[/tex]
Solving the operations:
[tex]0.71=c[/tex]
Therefore, the value of "c" is 0.71
