Answer:
see explanation
Step-by-step explanation:
1
Using right ΔBCD and the tangent ratio to solve for BC
tan40° =
Multiply both sides by 20
20 × tan40° = BC
BC ≈ 16.8
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2
Using right ΔABC and the cosine ratio to solve for AB
cos30° = =
Multiply both sides by AB
AB cos30° = 30 ( divide both sides by cos30° )
AB = ≈ 34.6
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3
Using the tangent ratio
tanA = = , hence
A = ( ) ≈ 22.6°
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4
Using the sine ratio
sin58° =
Multiply both sides by x
x sin58° = 4 ( divide both sides by sin58° )
x = ≈ 4.7
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5
Any of the 3 trig ratios may be used here since all 3 sides are given.
Using the tangent ratio
tan58° =
Multiply both sides by x
x tan58° = 4 ( divide both sides by tan58° )
x = ≈ 2.5