Question

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

Answer 1

Answer:

D. a = 11.71 and b = 15.56

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Trigonometry

• All angles in a triangle add up to 180°

Pre-Calculus

• Law of Sines: $\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}$

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 ∠

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

Step 3: Find measure of b

1. Substitute:                    $\frac{sin(25)}{7} =\frac{sin(110)}{b}$
2. Cross-multiply:             $bsin(25)=7sin(110)$
3. Isolate b:                       $b=\frac{7sin(110)}{sin(25)}$
4. Evaluate:                       $b=15.5645$
5. Round:                          $b \approx 15.56$

Step 4: Find measure of a

1. Substitute:                    $\frac{sin(25)}{7} =\frac{sin(45)}{a}$
2. Cross-multiply:             $asin(25)=7sin(45)$
3. Isolate a:                       $a=\frac{7sin(45)}{sin(25)}$
4. Evaluate:                       $a=11.7121$
5. Round:                          $a \approx 11.71$