The greatest distance across the continental United States i

The greatest distance across the continental United States is a bit less than 5,000 km To fit a map on an 8.5 in. Times 11 in. piece of paper, what scale should you use? Give your answer in metric units. Show why your answer works. A triangle has angles 39 degree and 47 degree, and an included side length of 1.75 inch. What are the measures of the third angle and the other two sides? A tetrahedron is shown below. It has four faces and each face is an equilateral triangle. On the figure below, draw a cross section of the tetrahedron that is in the shape of a square. Three roads meet as shown in the diagram below. Local laws prohibit planting trees at corners where roads intersect at angle of less than 20 degree. Can a tree be planted at angle A? Why or why not?

Solution

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10)

Since the maximum length of the paper is 11 inches, hence we need to map atleast 5000kms on 11 inches

1 inch = 2.54 cm

Hence number of cm\'s = 11 * 2.54 = 27.94 cm

5000 kms <= 27.94 cm (on map scale)

Hence 1 cm must be mapped to close to 180 kms

11) Sum of angles of a triangle = 180 degree

39 + 47 + angle C = 180

86 + angle C = 180

angleC = 94 degree

Using sine law

a/sinA = b/sinB = c/sinC

b/sin(47) = 1.75/sin(94)

b = 1.282 inches

c = 1.103 inches