Question

Precalculus: Find correct to 2 decimal places. NOTE: The triangle is NOT drawn to scale.

Answer 1

We can break the triangle into smaller and bigger triangles.

For the smaller triangle, we can get the length of the base using the tan ratio:

`\tan\theta=(opp)/(adj)`

From the image, we have:

`\begin{gathered} \theta=68\degree \\ opp=80 \\ adj=? \end{gathered}`

Therefore, we have:

`\begin{gathered} \tan68=(80)/(adj) \\ adj=(80)/(\tan68) \\ adj=32.32 \end{gathered}`

For the bigger triangle, the base can be calculated using the same tan ratio but with the following parameters:

`\theta=23\degree`

Therefore, we have:

`\begin{gathered} \tan23=(80)/(adj) \\ adj=(80)/(\tan23) \\ adj=188.47 \end{gathered}`

From the image, we have that:

`32.32+x=188.47`

Therefore, we can solve for x as shown below:

`\begin{gathered} x=188.47-32.32 \\ x=156.15 \end{gathered}`

The value of x is 156.15 units.