Question

these triangles are similar. solve for x.
x = ?

Explanation:

Identify corresponding sides

To solve for \(x\), we must identify which sides correspond to each other in the two similar triangles.
In the larger triangle, the side of length \(16\) is adjacent to the angles \(56^\circ\) and \(82^\circ\).
In the smaller triangle, the side of length \(10\) is adjacent to the angles \(56^\circ\) and \(82^\circ\).
Therefore, the side of length \(16\) corresponds to the side of length \(10\).

Set up the similarity ratio

The side of length \(24\) in the larger triangle is opposite the \(56^\circ\) angle.
In the smaller triangle, the side of length \(x\) is opposite the \(56^\circ\) angle.
Therefore, the side of length \(24\) corresponds to the side of length \(x\).
We can set up a proportion using the ratio of corresponding sides:

$$\frac{16}{10} = \frac{24}{x}$$

Solve for x

We solve the proportion by cross-multiplying:

$$16 \cdot x = 24 \cdot 10$$

$$16x = 240$$

$$x = \frac{240}{16}$$

$$x = 15$$

Answer:

These triangles are similar. Solve for x.
\(x =\) <blank>15</blank>