9514 1404 393
Answer:
54.8 km
Step-by-step explanation:
The sketch and the applicable trig laws cannot be completed until we understand what the question is.
<u>Given</u>:
two boats travel for 3 hours at constant speeds of 22 and 29 km/h from a common point, their straight-line paths separated by an angle of 39°
<u>Find</u>:
the distance between the boats after 3 hours, to the nearest 10th km
<u>Solution</u>:
A diagram of the scenario is attached. The number next to each line is the distance it represents in km.
The distance (c) from B1 to B2 can be found using the law of cosines. We can use the formula ...
c² = a² +b² -2ab·cos(C)
where 'a' and 'b' are the distances from the dock to boat 1 and boat 2, respectively, and C is the angle between their paths as measured at the dock.
The distance of each boat from the dock is its speed in km/h multiplied by the travel time, 3 h.
c² = 66² +87² -2·66·87·cos(39°) ≈ 3000.2558
c ≈ √3000.2558 ≈ 54.77
The boats are about 54.8 km apart after 3 hours.
What geometric shape formed the original wall of the colosseum is oval
Center of circle is ( 1, 0).
Slope of normal passing though ( 1, 0 ) and ( 2, -5 ) is :
So, slope of tangent will be :
Equation of tangent :
Hence, this is the required solution.
In a parallogram the two angles on the same side ( Angle T and Angle C) equal 180 degrees
So we have 8x +29 + 2x +11 = 180
combine the like terms:
10x + 40 = 180
Subtract 40 from each side:
10x = 140
Divide each side by 10:
X = 140 /10
X = 14
Now we have X, replace X into the equation for angle C
2(14) +11 = 28 + 11 = 39 degrees
Answer:
The answer to your question is 8.5 m
Step-by-step explanation:
Data
angle = Ф = 12°
dept = 40 m
distance from the ship to the treasure = ?
Process
To solve this problem use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is tangent.
tan Ф = Opposite side / Adjacent side
-Solve for Opposite side
Opposite side = Adjacent side x tanФ
-Substitution
Opposite side = 40 x tan 12
-Simplification
Opposite side = 8.5 m
