The back of Tom's property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing
1 answer:
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Answer:
1250 square feet
Step-by-step explanation:
If x is the length of the side perpendicular to the creek, then the third side is (100 -2x) = 2(50 -x). The area is the product of length and width:
A = x(2)(50-x)
We observe that this is a quadratic function with zeros at x=0 and x=50. The vertex (maximum) of a quadratic function is on the line of symmetry, halfway between the zeros. The value of x there is (0 +50)/2 = 25.
Then the maximum area is ...
A = (25)(2)(50 -25) = 1250 . . . . square feet
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<em>Additional comment</em>
Note that half the length of the fence is used in one direction (parallel to the creek), and half is used in the other direction (perpendicular to the creek). This 50/50 split is the generic solution to all sorts of rectangular corral problems, with or without a creek, with or without internal partitions.
Half the fence is perpendicular to the other half. (If the costs are different in different directions, then the cost is what is split 50/50.)
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Answer:
<em>The height of the bullding is 717 ft</em>
Step-by-step explanation:
<u>Right Triangles</u>
The trigonometric ratios (sine, cosine, tangent, etc.) are defined as relations between the triangle's side lengths.
The tangent ratio for an internal angle A is:
The image below shows the situation where Ms. M wanted to estimate the height of the Republic Plaza building in downtown Denver.
The angle A is given by his phone's app as A= 82° and the distance from her location and the building is 100 ft. The angle formed by the building and the ground is 90°, thus the tangent ratio must be satisfied. The distance h is the opposite leg to angle A and 100 ft is the adjacent leg, thus:
Solving for h:
Computing:
h = 711.5 ft
We must add the height of Ms, M's eyes. The height of the building is
711.5 ft + 5 ft = 716.5 ft
The height of the building is 717 ft
