Download Problem of the Day: Solve the following problem using

Pre-Calculus/Trigonometry 3
Name:
Chapter 4 Section 8: Triangle Applications
Date:
Block:
Problem of the Day: Solve the following problem using the Law of Sines and/or the Law of Cosines. Be
sure to show all of your work to come to your final answer.
1.) A = 51; b = 40; c = 45
2.) a = 11; b = 13; c = 20
Helpful Hints for Solving Application Problems:
Tip#1:
Tip #2:
Tip #3:
Trigonometry and Bearings:
In surveying and navigation, directions are usually given in terms of
Definition:
.
Bearing
.
Examples:
S 35 E
N 80 W
N 45 E
Applications Practice
Below are several different types of application problems. Each problem can be solved using Right
Triangle Trigonometry, Law of Sines, or Law of Cosines. Solve each problem and show all necessary
work. Be sure to include any drawings if one is not already provided.
1. Surveying. A triangular parcel of ground has sides of lengths 725 feet, 650 feet, and 575 feet.
Find the measure of the largest angle.
2. A ship travels 40 miles due East and then changes direction. When the ship has traveled 30 miles
at this heading, it is 56 miles from its point of departure. Describe the bearing from point B to
point C in the figure.
3. A ship leaves port at noon and heads due west at 20 knots, or 20 nautical miles per hour. At 2p.m.
the ship changes course to N 54 W, as shown in the figure below. Calculate the ship’s bearing
and distance from the port of departure at 3 p.m.
4. Baseball. On a baseball diamond with 90-foot sides, the pitcher’s mound is 60.5 feet from home
plate. How far is it from the pitcher’s mound to third base?
5. Light Design. Determine the angle  in the design of the
streetlight shown in the figure.
6. Football. Your football has landed at the edge of the roof of your school building. When you are
25 feet from the base of the building, the angle of elevation to your football is 21. How high off
the ground is your football?
7. Softball. The pitcher’s mound on a women’s softball field is 43 feet
from home plate and the distance between the bases is 60 feet, as
shown in the figure. The pitcher’s mound is not halfway between
home plate and second base. How far is the pitcher’s mound from
first base?
8. Angle of Elevation. A 10 meter telephone pole casts a 17-meter
shadow directly down a slope when the angle of elevation of the
sun is 42. Find , the angle of elevation of the ground.
9. Shadow Length. The Leaning Tower of Pisa in Italy
is characterized by its tilt. The tower leans because it
was built on a layer of unstable soil – clay, sand, and
water. The tower is approximately 58.36 meters tall
from its foundation as shown below. The top of the
tower leans about 5.45 meters off center.
a. Calculate the angle of the lean of the tower.
b. Write  as a function of d and , where  is
the angle of elevation to the sun.
c. Use the Law of Sines to write an equation for
the length d of the shadow cast by the tower.
10. At a point 200 feet from the base of a building, the angle of
elevation to the bottom of a smokestack is 35, whereas the
angle of elevation to the top is 53, as shown in the figure.
Calculate the height s of the smoke stack alone.