Question

Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.

Answer 1

Applying trigonometric ratios, the missing segments lengths in the image attached below are: a = 8√3; b = 12.

The Trigonometric Ratios

• SOH is sin ∅ = opp/hyp
• CAH is cos ∅ = adj/hyp
• TOA is tan ∅ = opp/adj
• SOHCAHTOA is used to solve right triangles.

Given the right triangle in the mage attached below, we would find the missing sides as follows:

Find a:

Reference angle (∅) = 30°

opposite = 4√3

hypotenuse = a

• Apply SOH:

sin 30 = (4√3)/a

a = (4√3)/sin 30

a = (4√3)/(1/2) (sin 30 = 1/2)

a = (4√3)×2

a = 8√3

Find b:

Reference angle (∅) = 60°

opposite = b

adjacent = 4√3

• Apply TOA:

tan 60 = b/(4√3)

b = tan 60 × 4√3

b = √3 × 4√3

b = 12

Therefore, applying trigonometric ratios, the missing segments lengths in the image attached below are: a = 8√3; b = 12.

Learn more about trigonometric ratios on:

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