Question

these triangles are similar.
solve for x.
\\(x = ?\\)

Explanation:

Identify corresponding sides

Using the Similar Triangles knowledge point

• The larger triangle has angles \(61^\circ\) and \(84^\circ\). The side between these angles has length \(8\).
• The smaller triangle has angles \(61^\circ\) and \(84^\circ\). The side between these angles has length \(x\).
• Therefore, the side of length \(8\) corresponds to the side of length \(x\).

Set up the similarity ratio

Using the Corresponding Sides Ratio knowledge point

• The side opposite the \(84^\circ\) angle in the larger triangle has length \(14\).
• The side opposite the \(84^\circ\) angle in the smaller triangle has length \(7\).
• We set up the proportion:

$$ \frac{8}{x} = \frac{14}{7} $$

Solve for x

Using the Corresponding Sides Ratio knowledge point

$$
LATEXBLOCK0
$$

Answer:

These triangles are similar. Solve for x.

\(x =\) <blank>4</blank>