Download Lesson 6-2 Practice - Mayfield City Schools

Math 2 Honors
Lesson 6-2 Practice
Name________________________
1. Terri is flying a kite and has let out 500 feet of string. Her end of the string is 3 feet off the ground.
a. If KIT has a measure of 40, approximately how high
off the ground is the kite?
b. As the wind picks up, Terri is able to fly the kite at a
56 angle with the horizontal. Approximately how
high is the kite?
c. What is the highest Terri could fly the kite on 500 feet of string? What would be the measure of
KIT then?
d. Your answers in Parts a-c are estimates. When you actually fly a kite, what are some factors that
might cause your answers to be somewhat inaccurate?
2. In Fort Recovery, Ohio, there is a monument to local soldiers who died in battle. Mr. Knapke, a
teacher at the local high school, challenged his class to find as many ways as they could to measure
the height of the monument indirectly.
Pedro, whose eye level P is 5.8 feet, proposed a novel solution. He placed a mirror M on the ground
45 feet from the center of the monument’s base and then moved to a point 2.6 feet further from the
monument where he could just see to the top of the monument in the mirror. He recalled from his
earlier studies that the angle of incidence and the angle of reflection are congruent.
a. Show all of the given information on the above diagram.
b. Figure out how Pedro found the height of the monument. What is the height?
c. Describe another method to find the height of the monument.
3. A survey team was to measure the distance across a river over which a bridge is to be built. They set
up a survey post on their side of the river directly across from a large tree on the other side. Then
they walked downstream a distance that they measured to be 400 meters. From the downstream
position, they sighted the survey post and then rotated their calibrated transit to the tree to find the
sighting angle to be 31.
a. Determine the distance directly across the river, that is, from the survey post to the tree on the
opposite bank.
b. Determine the distance from the surveyors’ sighting point to the tree on the opposite bank.
4. The diagram below shows a portion of a circle with radius 1 and center at the origin. Point A’ is the
image of point A and point B’ is the image of point B under a 30 counterclockwise rotation about
the origin.
a. Explain why the coordinates of point A’ are (cos 30, sin 30).
b. What is the length of OB ? Why?
i.
Write the x-coordinate a of point B’ as a trigonometric function of 30.
ii.
Write the y-coordinate b of point B’ as a trigonometric function of 30.
5. A surveyor made a sighting to the top of a mountain peak from point A, located on a flat plateau.
The angle of elevation from point A was 28. He then moved 200 feet directly toward the mountain
to point B on the same plateau. The angle of elevation from point B was 39. Find the height of the
mountain peak above the plateau. Draw a figure, and show your work.
6. Carl and Lisa are both drawing triangles ABC that meet each set of criteria below. Must the triangles
they draw be congruent? Explain your reasoning.
a. The lengths of the three sides are 3 cm, 8 cm, and 7 cm.
b. The measures of the three angles are 120, 20, and 40.
c. AB = 5 in, mB  60, and mA  50
d. mC  100, BC = 10 cm, and AC = 8 cm
e. mB  35, BC = 10 in, AC = 8.5 in
7. Find the area of ABC in each diagram.
a.
b.
c.
d.