In the smallest of the three triangles (with sides ) we have
In the second-largest triangle (with sides ), the length of the missing side is
. Then in the largest triangle (with sides
), we have
Equivalently, we have
In turn, we find
The school is 100 meters from Miguel's house.
1 answer:
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Answer:
(3 square root of 2 , 135°), (-3 square root of 2 , 315°)
Step-by-step explanation:
Hello!
We need to determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.
We know that the polar coordinate system is a two-dimensional coordinate. The two dimensions are:
- The radial coordinate which is often denoted by r.
- The angular coordinate by θ.
So we need to find r and θ. So we know that:
(1)
x = rcos(θ) (2)
x = rsin(θ) (3)
From the statement we know that (x, y) = (3, -3).
Using the equation (1) we find that:
Using the equations (2) and (3) we find that:
3 = rcos(θ)
-3 = rsin(θ)
Solving the system of equations:
θ= -45
Then:
r = 3\sqrt{2}[/tex]
θ= -45 or 315
Notice that there are two feasible angles, they both have a tangent of -1. The X will take the positive value, and Y the negative one.
So, the solution is:
(3 square root of 2 , 135°), (-3 square root of 2 , 315°)
Change it into improper fraction to make it easier or just solve it as is.
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OR
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divide it to two parts:
3-2=1 and
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⇒(1×8-2=6)
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OR
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divide it to two parts:
3-2=1 and
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