The area of a rectangular patio is 558 square yards, and its length is 112 yards. What is the patio’s width, in yards?
1 answer:
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1. Given any triangle ABC with sides BC=a, AC=b and AB=c, the following are true :
i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.
ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:
2.
3. m(A) = Arccos(-0.641)≈130°,
4. Remark: We calculate Arccos with a scientific calculator or computer software unless it is one of the well known values, ex Arccos(0.5)=60°, Arccos(-0.5)=120° etc
i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.
ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:
2.
3. m(A) = Arccos(-0.641)≈130°,
4. Remark: We calculate Arccos with a scientific calculator or computer software unless it is one of the well known values, ex Arccos(0.5)=60°, Arccos(-0.5)=120° etc
We know that:
is an equation of a circle.
When we substitute x and y (from the pairs we have), we'll get a system of equations:
and all we have to do is solve it for a, b and r.
There will be:
From equations (II) and (III) we have:
and from (I) and (II):
Now we can easly calculate a and b:
Finally we calculate
:
And the equation of the circle is:
is an equation of a circle.
When we substitute x and y (from the pairs we have), we'll get a system of equations:
and all we have to do is solve it for a, b and r.
There will be:
From equations (II) and (III) we have:
and from (I) and (II):
Now we can easly calculate a and b:
Finally we calculate
And the equation of the circle is: