Set up a right triangle model for this problem and solve by using the reference table trigonometric ratio that applies. Follow t
2 answers:
Answer: B. 52.2 yards
Lighthouse is 52.2 yards tall.
Step-by-step explanation:
Let AB denotes the height of the lighthouse & BC denotes the distance between the base of a lighthouse and Photographer.
In Figure, ∠ACB = 41° & ∠ABC = 90°, Threrefore, Base is BC and perpendicular is AB.
As we know, tan(∠ACB) =
∴ tan 41° =
tan 41° =
0.869286737 =
AB = 52.2 yards ( approx.)
Thus, Height of the lighthouse is 52.2 yards
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The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :
Length of transverse axis is :
length of conjugate axis is :
Equation of hyperbola ~
plug in the values ~
From the problem, the vertex = (0, 0) and the focus = (0, 3)
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12
Source:
http://www.1728.org/quadr4.htm
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12
Source:
http://www.1728.org/quadr4.htm