Question

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

Answer 1

`\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 (sin(A))/(a) =(sin(B))/(b) =(sin(C))/(c)`

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

Explanation:

Step 1: Identify

A = 27°, a = 11

B = x°, b = 15

Step 2: Solve for x

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