Download 4-7 Word Problem Practice The Law of Sines and the Law of Cosines

NAME
DATE
4-7
PERIOD
Word Problem Practice
The Law of Sines and the Law of Cosines
1. ART Local artists are painting barn
quilts at a Community Center. The quilts
are each 8 feet by 8 feet. The symmetrical
pattern for a particular barn quilt is
shown below.
4. BLIMP A blimp hovers over a soccer
stadium. Players 500 feet apart at opposite
ends of the stadium with the blimp
between them measure the respective
angles of elevation to the blimp to be 63°
and 72°. How high is the blimp?
599.2 ft
red
blue
45°
100°
yellow
6.5 ft
green
63°
a. What is the area of the yellow
triangle? 16.9 ft 2
72°
500 ft
5. AVIATION Due to weather conditions,
an airplane flies in different directions
as shown in the diagram.
b. It takes three coats of paint to make a
barn quilt. If it takes 3.5 ounces of
paint to cover a square foot, how
much paint will be needed for the
yellow triangle? 177.5 oz
80 mi
Destination
City
110°
145 mi
2. ARCHITECTURE The roof on a house
has one side that is in the shape of an
isosceles triangle. If the sides of this
part are 18 feet long and the angle at
the peak is 50°, what is the area of this
part of the roof? 124.1 ft2
Start
b. What are the measures of the two other
angles in the triangle? 23.6°, 46.4°
3. ORIENTEERING During an orienteering
exercise, two hikers start at point A and
head in a direction 30° west of south to
point B. They hike 6 miles from point A
to point B. From point B, they hike to
point C and then from point C back to
point A, which is 8 miles directly north of
point C. How many miles did they hike
from point B to point C?
6. PROPERTY MAINTENANCE The
McSweeneys plan to fence a triangular
parcel of their land. One side of the
property is 75 feet in length and forms
a 38° angle with another side of the
property, which has not yet been
measured. The remaining side of the
property is 95 feet in length.
Approximate to the nearest tenth the
length of fence needed to enclose this
parcel of the McSweeneys’ lot.
"
30°
6 mi
about 312.1 ft
#
4.1 mi
Chapter 4
8 mi
7. SHIP A ship at sea is 92 miles from one
radio tower and 124 miles from another.
The angle between the radio signals has
a measure of 156°. Find the distance
between the radio towers. 211.4 mi
$
40
Glencoe Precalculus
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
a. How far is the airport from the
destination city if the direct route is
taken? 188 mi