Question

Help with trigonometry. (Ignore the writing I still need all of them)

Answer 1

Applying the trigonometry ratio and rationalization, the missing lengths are:

1. x = 12/√3; y = 2√3

2. x = 5√2; y = 5√2

3. b = 24

4. 4√3

5. 5√3

What are the Trigonometry Ratio?

The trigonometry ratios are represented as follow:

• SOH is sin ∅ = opp/hyp
• CAH is cos ∅ = adj/hyp
• TOA is tan ∅ = opp/adj.

1. To find x, apply SOH:

opp = 6

hyp = x

adj = y

∅ = 60°

Equation:

sin 60 = 6/x

x = 6/sin 60

x = 6/√3/2 (sin 60 = √3/2)

x = 6 × 2/√3

x = 12/√3

Rationalize

x = 12/√3 × √3 /√3

x = 12√3/3

x = 4√3

To find y, apply TOA:

tan 60 = 6/y

y = 6/tan 60

y = 6/√3 (tan 60 = √3)

Rationalize

y = 6/√3 × √3 /√3

y = 6√3 / 3

y = 2√3

2. To find x, apply SOH:

opp = x

hyp = 10

adj = y

∅ = 45°

Equation:

sin 45 = x/10

x = (10)(sin 45)

x = 10 × 1/√2 (sin 45 = 1/√2)

x = 10/√2

Rationalize

x = 10/√2 × √2 /√2

x = 10√2/2

x = 5√2

To find y, apply CAH:

cos 45 = y/10

y = (10)(cos 45)

y = 10 × 1/√2 (cos 45 = 1/√2)

y = 10/√2

Rationalize

y = 10/√2 × √2 /√2

y = 10√2/2

y = 5√2

3. To find b, apply Pythagorean theorem:

b = √(25² - 7²)

b = 24

4. 12/√3

Rationalize

12/√3 × √3 /√3

12√3/3

4√3

5. 15/√3 × √3 /√3

15√3 /3

5√3

Learn more about trigonometry ratios on:

brainly.com/question/10417664