On Monday, it took Helen 3 hours to do a page of science homework exercises. The next day she did the same number of exercises i
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Given
∆PQR points are P(-2,5), Q(-1,1), and R(7,3)
Determine whether ∆PQR is a right triangle
To proof
As given ∆PQR points are P(-2,5), Q(-1,1), and R(7,3)
First find out the sides of triangle
FORMULA
Distance formula between two points
Distance between two points P(-2,5) and Q(-1,1)
Distance between two points Q(-1,1)and R(7,3)
Distance between two points R(7,3) and P(-2,5)
now show that ∆PQR is a right triangle
Putting the value given above
85 = 17 +68
85 =85
In the right triangle
HYPOTENUSE² = BASE² + PERPENDICULAR²
This is prove above
Hence ∆PQR is a right triangle
Hence proved
Answer: Approximately 8.49 feet
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Explanation:
Draw a right triangle. The reference angle is between the ground and the kite string (aka hypotenuse). The hypotenuse is 12 and the side opposite the reference angle is x.
Refer to the diagram below.
We'll use the sine rule to find x
sin(angle) = opposite/hypotenuse
sin(45) = x/12
12*sin(45) = x
x = 12*sin(45)
x = 8.48528137423857
x = 8.49
This value is approximate.
Make sure your calculator is in degree mode.
I rounded to 2 decimal places, but feel free to round however you need if your teacher instructs otherwise.
