Harvard University Math Worksheet

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QUESTION 1
1.
A 6-foot ladder is leaning against a wall. The base of the ladder is 2 feet from the base of the
wall. What is the approximate angle of elevation between the ladder and the ground?
50¶0·0¸0±0 points
QUESTION 2
1.
A camera is at ground level 20 feet away from a building and focusing on a point 200 feet high. What
is the approximate angle of elevation of the camera?
78±5·3¸4±0 points
QUESTION 3
1.
Calculate the magnitude of vector u = .
12
9
5
16
10 points
QUESTION 4
1.
Convert the angle measure 2884o radians.
1.3?
1.4?
1.5?
1.6?
10 points
QUESTION 5
1.
Given a = 12, b = 15, and c = 16, use the Law of Cosines to find angle C. Round to three decimal
places.
45.406¶2.888·1.706¶0.717±0 points
QUESTION 6
1.
Given vectors u = and v = , find the resultant vector u + v.
10 points
QUESTION 7
1.
Simplify the equation cos (? – x).
sin x
cos x
– sin x
– cos x
10 points
QUESTION 8
1.
The monthly sales S (in hundreds of units) of skiing equipment at a sports store are approximated by
S = 58.3 + 32.5 cos (t?/6), where t is the time (in months), with t = 1 corresponding to
January. Determine the month with lowest sales.
May
June
July
August
10 points
QUESTION 9
1.
The sun is 60!bove the horizon. If a building casts a shadow 230 feet long, approximately how tall
is the building?
400 feet
130 feet
230 feet
80 feet
10 points
QUESTION 10
1.
What is the range of 2 tan(x – ?/6)?
[-1, 1]
[-2, 2]
(-?, ?)
[-0.866, 0.866]
QUESTION 11
1.
A camera is at ground level 20 feet away from a building and focusing on a point 100 feet high. What
is the approximate angle of elevation of the camera?
5
22´5·9±0 points
QUESTION 12
1.
Given sin u = 0.5 and cos u = 0.866, find tan u.
30¶0°.5
0.577

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