Answer:
- Maria–Ava: 15.7 feet
- Lucas–Maria: 10.1 feet
- angle at Maria: 50°
Step-by-step explanation:
The cosine and tangent functions are useful here. The relevant relations are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
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The distance from Maria to Ava (ma) is the hypotenuse of the triangle, so we have ...
cos(40°) = 12/ma
ma = 12/cos(40°) ≈ 12/0.76604 ≈ 15.7 . . . feet
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The distance from Lucas to Maria (ml) is the side opposite the given angle, so we have ...
tan(40°) = ml/12
ml = 12·tan(40°) ≈ 12·0.83910 ≈ 10.1 . . . feet
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The angle formed at Maria's position is the complement of the other acute angle in the right triangle:
M = 90° -40° = 50°
In summary, ...
- Maria–Ava: 15.7 feet
- Lucas–Maria: 10.1 feet
- angle at Maria: 50°
