Work out the length x in the triangle below.
1 answer:
Answer:
x = 8
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = absinC
where a and b are 2 sides of the triangle and C the angle between them
here a = 13 , b = x , C = 30° and A = 26 , then
× 13 × x × sin30° = 26 ( multiply both sides by 2 to clear the fraction )
13x × sin30° = 52 ( using the exact value of sin30° = )
13x × = 52 ( multiply both sides by 2 to clear the fraction )
13x = 104 ( divide both sides by 13 )
x = 8
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Answer:
The largest total area that can be enclosed will be a square of length 272 yards.
Step-by-step explanation:
First we get the perimeter of the large rectangular enclosure.
Perimeter of a rectangle =2(l + w)
Perimeter of the large rectangular enclosure= 1088 yard
Therefore:
2(L+W)=1088
The region inside the fence is the area
Area: A = LW
We need to solve the perimeter formula for either the length or width.
2L+ 2W= 1088 yd
2W= 1088– 2L
W =
W = 544–L
Now substitute W = 544–L into the area formula
A = LW
A = L(544 – L)
A = 544L–L²
Since A is a quadratic expression, we re-write the expression with the exponents in descending order.
A = –L²+544L
Next, we look for the value of the x coordinate
L=272 yards
Plugging L=272 yards into the calculation for area:
A = –L²+544L
A(272)=-272²+544(272)
=73984 square yards
Thus the largest area that could be encompassed would be a square where each side has a length of 272 yards and a width of:
W = 544 – L
= 544 – 272
= 272 yards