A patio is to be made in the shape of an isosceles triangle as shown.
1 answer:
9514 1404 393
Answer:
(a) 22 is not the correct value of h
(b) 164 ft²
(c) $2009
Step-by-step explanation:
(a) Apparently, the formula ...
A = 1/2bh
was used. We recognize the base of the triangle is 16 feet, so apparently the formula was used with h=22.
22 is the side length, not the perpendicular distance from the base to the opposite vertex.
The computed value is not the area because 22 is not the height.
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(b) Given three side lengths, an appropriate formula is Heron's formula:
s = (a+b+c)/2 and A = √(s(s-a)(s-b)(s-c))
Here, we have ...
s = (22 +22 +16)/2 = 30 and A = √(30(8)(8)(14) = 16√105 ≈ 163.95
The area is about 164 square feet.
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(c) At $12.25 per square foot, the cost of materials will be ...
(164 ft²)($12.25/ft²) = $2009
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Did two of them for you as reference for the rest.
Explanation for #1
The sum of all the angles in a triangle is 180. Simply add the given angles. Take 180 and subtract the sum of the given angles
180 - (58 + 47) = 75
Missing angle is 75
Explanation for #4
A straight angle is 180 degrees. Same thing as the first: add the given angles then take 180 and subtract it.
Then take 180 <em>again </em>and subtract the answer you got from the first step.
180 - (21 + 34) = 125
180 - 125 = 55
The missing angle is 55
