Question

Solve the right angle trig problem.

Answer 1

9514 1404 393

Answer:

• x ≈ 9.24
• H ≈ 11.02

Explanation:

The mnemonic SOH CAH TOA reminds you of the relationships.

Tan = Opposite/Adjacent

tan(57°) = x/6

x = 6·tan(57°) ≈ 9.24

__

The complete solution of the triangle will also find a value for H.

Cos = Adjacent/Hypotenuse

cos(57°) = 6/H

H = 6/cos(57°) ≈ 11.02

_____

Comment on the figure

We note that, in relation to the given angle, the markings O and A are reversed. The side labeled 6 is adjacent (A) to the marked angle, and the side labeled x is opposite (O) to the marked angle.

Answer 2

x = 9.23919

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

Trigonometry

• [Right Triangles Only] SOHCAHTOA
• [Right Triangles Only] tan∅ = opposite over adjacent

Explanation:

Step 1: Define

We are given a right triangle. We can use trig to find the missing length.

Step 2: Identify Variables

POV from the angle measure

Angle = 57°

Opposite = x

Adjacent = 6

Step 3: Solve for x

1. Substitute: tan57° = x/6
2. Isolate x: 6tan57° = x
3. Evaluate: 9.23919 = x
4. Rewrite: x = 9.23919