An observer from the top of a lighthouse 370 feet above sea level sees two sailboats in the water. The angles of depression to t
he boats are 12 degrees and 10 degrees. How far apart are the boats, to the nearest foot?
1 answer:
Answer:the sailboats are 358 feet apart.
Step-by-step explanation:
The diagram of the triangle representing the situation is shown in the attached photo.
B represents the position of the lighthouse.
D represents the position of the first sailboat.
C represents the position of the second sailboat.
x represents the distance between the two sailboats
We would apply trigonometric ratio
Tan # = opposite/adjacent
For triangle ABD,
Tan 12 = 370/AD
AD = 370/Tan 12 = 370/0.2126 = 1740.357 feet
For triangle ABC,
Tan 10 = 370/AC
AD = 370/Tan 10 = 370/0.1763 = 2098.695 feet
x = AC - AD = 2098.695 - 1740.357 = 358 feet
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Answer:
The graph of f(x) is shifted up 50 units
The graph of f(x) is shifted right 10 units
The graph of f(x) is reflected over the x-axis
Step-by-step explanation:
we have
This is a vertical parabola open upward
The vertex is a minimum
The vertex is the origin (0,0)
This is a vertical parabola open downward
The vertex is a maximum
The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.
Find the vertex of g(x)
Convert to vertex form
Complete the square
The vertex is the point (10,50)
so
To translate the vertex of (0,0) to (10,50)
The rule of the translation is
(x,y) ------> (x+10,y+50)
That means ----> The translation is 10 units at right and 50 units up
therefore
The transformations are
The graph of f(x) is shifted up 50 units
The graph of f(x) is shifted right 10 units
The graph of f(x) is reflected over the x-axis