9514 1404 393
Answer:
- red boat distance: 42 miles
- angle at lighthouse: 22°
Step-by-step explanation:
The Law of Cosines can be used to find the distance from the red boat to the lighthouse.
b² = l² +r² -2lr·cos(B)
b² = 18² +30² +2·18·30·cos(120°) = 1764
b = √1764 = 42
The distance from the red boat to the lighthouse is 42 miles.
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The angle at the lighthouse can be found using the law of sines.
sin(L)/l = sin(B)/b
L = arcsin(l/b·sin(B)) = arcsin(18/42·sin(120°)) ≈ 21.79°
The angle between the boats measured at the lighthouse is about 22°.
<h3>
Answer:</h3>
1 27/28 ≈ 1.964 gallons/hour
<h3>
Step-by-step explanation:</h3>
You want gallons in the numerator of your unit rate, but that unit is in the denominator of the mileage rate. So, the computation must involve division by 28 mpg. Hours is already in the denominator of 55 mph, so the computation will involve multiplication by that rate.
... (55 mi/h)/(28 mi/gal) = (55 mi/h)·(1 gal/(28 mi)) = 55/28 gal/h
... = 1 27/28 gal/h
Answer:
Step-by-step explanation:
<-- Given
<-- Multiply by the conjugate of the denominator as a factor of 1
<-- Use the Distributive Property and FOIL
<-- Rewrite 
as 
<-- Rewrite in 
form
Answer:
1. Find < ACB
2. Use that triangles =180 to find <B = 41
Step-by-step explanation:
1.We need to find < ACB
<ACB +<DBC= 180 They make a straight line
Subtract DBC from each side
<ACB = 180 - <DBC
We know DCB = 113
ACB = 180 -113
ACB = 67
2.The three angles of a triangle = 180, so we can then find <B
<A +<B + <ACB = 180
72 + B + 67 = 180
Combine like terms
139+ <B = 180
Subtract 139 from each side
<B = 180-139
<B =41
