Calculate the side lengths a and b to two decimal places.

D. a = 11.71 and b = 15.56

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Trigonometry

All angles in a triangle add up to 180°

Pre-Calculus

Law of Sines:

Step-by-step explanation:

Step 1: Define

AC = b

CB = a

AB = 7

m∠A = 45°

m∠B = 110°

m∠C = ?

Step 2: Find missing ∠

Set up equation:                    m∠C + 45° + 110° = 180°Combine like terms:              m∠C + 115° = 180°Isolate unknown:                   m∠C = 25°

Step 3: Find measure of b

Substitute:                    Cross-multiply:             Isolate b:                       Evaluate:                       Round:                          

Step 4: Find measure of a

Substitute:                    Cross-multiply:             Isolate a:                       Evaluate:                       Round:                          

The answer is all about the number 4