Question

these triangles are similar.
solve for x.

\\x = ?\\

Explanation:

Identify corresponding parts of the similar triangles

Using the Similar Triangles knowledge point

• The larger triangle has angles \(93^\circ\) and \(20^\circ\).
• The smaller triangle has angles \(93^\circ\) and \(20^\circ\).
• In the larger triangle, the side of length \(12\) is opposite the \(20^\circ\) angle.
• In the smaller triangle, the side of length \(x\) is opposite the \(20^\circ\) angle.
• In the larger triangle, the side of length \(24\) is opposite the third angle.
• In the smaller triangle, the side of length \(16\) is opposite the third angle.

Set up the proportion for corresponding sides

Using the Corresponding Sides Ratio knowledge point

$$ \frac{\text{Side opposite } 20^\circ \text{ in smaller triangle}}{\text{Side opposite } 20^\circ \text{ in larger triangle}} = \frac{\text{Side opposite third angle in smaller triangle}}{\text{Side opposite third angle in larger triangle}} $$

$$ \frac{x}{12} = \frac{16}{24} $$

Solve the equation for x

Using the Corresponding Sides Ratio knowledge point

$$
LATEXBLOCK0
$$

Answer:

These triangles are similar. Solve for x.

\(x =\) <blank>8</blank>