UNIT 3 SAMPLE WORK TRIGONOMETRY PILE UP
Solve for X

First of all, yuck.

• Start from the bottom, in ∆1:

sin(30°) = 4 / (a₁ + 2.5)   →   a₁ = 4 / sin(30°) - 2.5 = 5.5

where a₁ is the part of the hypotenuse of ∆1 that overlaps with the hypotenuse of ∆2.

• In ∆2:

cos(15°) = (2.2 + a₂) / (3.5 + a₁)   →   a₂ = (3.5 + a₁) cos(15°) - 2.2 ≈ 6.493

where a₂ is the part of the leg of ∆2 that overlaps with the hypotenuse of ∆3.

• In ∆3:

a₃² + 3.5² = (a₂ + 2.4)²   →   a₃ = √((a₂ + 2.4)² - 3.5²) ≈ 8.176

where a₃ is the leg of ∆3 that overlaps with ∆4 and ∆5.

• In ∆4:

tan(51°) = a₄ / 2.855   →   a₄ = 2.855 tan(51°) ≈ 3.526

where a₄ is the leg of ∆4 that overlaps with the leg of ∆5.

• In ∆5:

The overlapping legs of ∆4 and ∆5 have the same length, so

sin(48°) = a₄ / a₅   →   a₅ = a₄ / sin(48°) ≈ 4.744

where a₅ is the hypotenuse of ∆5.

• In ∆9:

sin(58°) = (a₆ + 2.5) / (4.18 + a₅)   →   a₆ = (4.18 + a₅) sin(58°) - 2.5 ≈ 5.068

where a₆ is the leg of ∆10 that overlaps with the leg of ∆9.

• In ∆10:

a₇² = 2.2² + a₆²   →   a₇ = √(2.2² + a₆²) ≈ 5.525

where a₇ is the hypotenuse of ∆10.

• In ∆11:

cos(21°) = a₇ / a₈   →   a₈ = a₇ / cos(21°) ≈ 5.918

where a₈ is the hypotenuse of ∆11.

• In ∆12: (finally!)

sin(74°) = x / (a₈ + 2.6)   →   x = (a₈ + 2.6) sin(74°) ≈ 8.19

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

ok so the answer to your question is simple as long as you look at the different dimensions that contain the exemplary letters that combined in the right order give you words that eventually within the 5th dimension will conform and give you the correct answer to your question. hope i , stop looking at this easily, look at it with a spectral view.

step-by-step explanation:

told you