Homework #8
Pre Calculus
Due 10/28/08
Name:
Period
Date:
For each problem, draw a clear diagram, label it with relevant information, and use a
variable (which you put in your diagram) for each piece of information that you are trying to
determine. Check to see if your answer is reasonable!
1. A surveyor is measuring the height of a
mountain. The angle of elevation of the
mountain peak from point A is 30
degrees. The angle of elevation from
point B is 30.7 degrees. A and B are
1100 feet apart. How high is the
mountain?
2. A plane flies 500 miles per hour in an exactly northwesterly direction. How far is it traveling in a
westerly direction each hour? What is its northward speed?
3. A father pulls his son back on a swing. When the boy was hanging straight down, the swing
was .6 meters above the ground. When the father pulled the son back at a 30° angle (as
measured at the top of the swing), the boy was 1.5 meters above the ground. How long is the
swing’s chain?
4. An isosceles trapezoid has sides of length 6, 7, 8, and 7. Find its area, angle measures, and
the length of its diagonals.
5. Amanda is doing pushups. With her 2foot long arms extended, her body makes a 28º angle
with the floor. How far are her hands from her feet?
6. You are swimming along in the ocean. 23 meter behind you and 17 meters below the surface,
Jaws the shark is swimming level in the same direction. If the shark’s field of vision includes
anything up to 33º above a level line of sight, will you be safe or will you be fish food?
7. Find all x (in radians) for which cos(sin(x)) =1
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8. The great pyramid of Cheops is 775 feet on each edge of its square base and 481 feet high.
What angle does each wall make with the base?
9. Two hikers at different locations (they are at opposite sides of the tree) see the famous
“General Sherman” sequoia from a distance. Each uses her handy protractor to measures the
angle of elevation to the top of the tree. One hiker measures the angle of elevation to be 65
and the other measures the angle of elevation to be 50. A plaque at the base of the tree gives
the height to be 275 feet. How far apart were the hikers from each other when they made their
measurements?
10. In each of the following diagrams, find the reference angle and list an angle from each quadrant
(three angles total) that have the same reference angle.
200o
282o
11. Consider the diagrams below. Both circles have the same radius and point P is located at
(8, 15). The angle θ has the same measurement in both diagrams.
P
Q



a. Find the angle θ and the length of the radius of the circle.
b. Find the coordinates of point Q and the measure of angle α.
c. Evaluate sin(α) and cos(α). Express answers as exact fractions.
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