Question

Find the value of x. Round to the nearest tenth.

Answer 1

Answer:

$\displaystyle x \approx 38.2 ^{\circ}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtract Property of Equality

Pre-Calculus

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

• A, B, C are angle measures
• a, b, c are leg lengths

Step-by-step explanation:

Step 1: Identify

A = 27°, a = 11

B = x°, b = 15

Step 2: Solve for x

1. Substitute [LOS]:                     $\displaystyle \frac{sin(27^{\circ})}{11} =\frac{sin(x^{\circ})}{15}$
2. Cross-multiply:                        $\displaystyle 11sin(x^{\circ}) = 15sin(27^{\circ})$
3. Isolate x term:                         $\displaystyle sin(x^{\circ}) = \frac{15sin(27^{\circ})}{11}$
4. Isolate x:                                  $\displaystyle x = sin^{-1}(\frac{15sin(27)}{11})$
5. Evaluate:                                 $\displaystyle x = 38.2488 ^{\circ}$
6. Round:                                    $\displaystyle x \approx 38.2 ^{\circ}$