Giulia unreels her kite string until the kite is flying on a string of length 50 m. A light breeze holds the kite such that the
string makes an angle of 60° with the ground. After a few minutes, the wind picks up speed. The wind now pushes the kite until the string makes an angle of 45° with the ground. What distance has the kite changed position horizontally over the ground. Determine an exact expression.
1 answer:
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Answer:
x = 3
Step-by-step explanation:
We require the equations of the 2 lines.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
The line has slope = 7, hence
y = 7x + c ← is the partial equation
To find c substitute (6, 28) into the partial equation
28 = 42 + c ⇒ c = 28 - 42 = - 14
y = 7x - 14 → (1)
Calculate the slope of the second line using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 7) and (x₂, y₂ ) = (- 1, - 13)
m = =
= 5, thus
y = 5x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 7), then
7 = 15 + c ⇒ c = 7 - 15 = - 8
y = 5x - 8 → (2)
Solving (1) and (2) by equating the right sides
7x - 14 = 5x - 8 ( subtract 5x from both sides )
2x - 14 = - 8 ( add 14 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3
The x- coordinate of the point of intersection is x = 3