Question

express x in terms of a, b, and c.
x =
diagram: a triangle with a smaller similar triangle inside, sides labeled c, b, a, angles labeled x

Explanation:

Step1: Identify Similar Triangles

The two triangles are similar (AA similarity, as they share the same angle and have a right angle or equal angles marked \( x \)). So, the ratios of corresponding sides are equal.

Step2: Set Up Proportion

For similar triangles, \(\frac{x}{a}=\frac{c}{b}\) (corresponding sides of similar triangles are proportional).

Step3: Solve for \( x \)

Cross - multiply to get \( x\times b=a\times c \), then \( x = \frac{ac}{b} \).

Answer:

\(\frac{ac}{b}\)