## Math Problem Statement

A student begins a proof of the law of cosines. His work is shown.

The next step in the proof is to write an expression for the length of side AZ in terms of x, z, and Zy, z, and Xy, z, and Y.

Then the student should write an expression for the length of side AY in terms of z and Xx and Zz and Y.

Next he can use the Pythagorean theoremtangent functionlaw of sines to relate *x*, *y*, *z*, and XZY.

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## Solution

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## Math Problem Analysis

### Mathematical Concepts

Trigonometry

Geometry

Law of Cosines

### Formulas

Law of Cosines: c^2 = a^2 + b^2 - 2ab * cos(C)

Pythagorean Theorem: a^2 + b^2 = c^2 (for right triangles)

Tangent Function: tan(θ) = opposite/adjacent

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

### Theorems

Law of Cosines

Pythagorean Theorem

Law of Sines

### Suitable Grade Level

Grades 9-12