Question

Please solve using pre-calculus and leave answers in decimal form.

Answer 1

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:

`\tan \theta=(opposite)/(adjacent)`

Substituting we get:

`\tan 15=(a)/(1)`

Solving the operations:

`a=\tan 15\approx0.28`

Now, we will determine the value of "b" using the larger triangle, as shown next:

We will use tangent:

`\tan 15=(1)/(b+a+a+a+a)`

Adding like terms:

`\tan 15=(1)/(b+4a)`

Now, we solve for "b". To do that, we will invert both sides:

`(1)/(\tan 15)=b+4a`

Now, we subtract "4a" from both sides:

`(1)/(\tan 15)-4a=b`

Now, we substitute the value of "a":

`(1)/(\tan15)-4\tan 15=b`

Solving the operations:

`2.66=b`

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:

`\tan 15=(c)/(b)`

We multiply both sides by "b":

`b\tan 15=c`

Substituting the values:

`2.66\tan 15=c`

Solving the operations:

`0.71=c`

Therefore, the value of "c" is 0.71