Applying trigonometric ratios, the missing segments lengths in the image attached below are: <em>a = 8√3; b = 12.</em>
<h3>The Trigonometric Ratios</h3>- 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:
<em>Find a:</em>
Reference angle (∅) = 30°
opposite = 4√3
hypotenuse = a
- <em>Apply SOH:</em>
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
<em>Find b:</em>
Reference angle (∅) = 60°
opposite = b
adjacent = 4√3
- <em>Apply TOA:</em>
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: <em>a = 8√3; b = 12.</em>
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