Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
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Therefore, the angle between their paths is <em>100.8°</em>
Writing it as a decimal would be 3.85 you just divide it
Answer:
312
Step-by-step explanation:
Volume of the parallalelepiped:
base x width x height
V = 5 x 4 x 12 = 240
for triangular prism:
base = 8-5 = 3
base area = (base x height)/2 = (3x4)/2 = 6
V = base area x 12
V = 6 x 12 = 72
Total volume = 240 + 72 = 312