Download MA 42 Chapter 6 Test Review B

MA42: TRIGONOMETRY
HOMEWORK
LAW OF SINES & COSINES – EXAM REVIEW #01
Name:
Date:
1. Solve ABC , given A  71, B  42, c  15
2. Solve ABC , given A  67, a  100, c  125
3. Can you use the Law of Sines to solve ABC if A  40, b  10, c  20 ? Explain.
4. DISTANCE ACROSS A CANYON: To determine the distance RS across a deep canyon. Joanna lays
off a distance TR = 582 yards on her side of the canyon. She then finds that T = 32º 50’ and
R = 102º 20’. Find the distance across the canyon, RS.
5. DISTANCE TO SHIPS: Three ships are within site of each other. The Maverick spots the two other
ships, the Northern-Star and the Throw-Rug, and measures the angle between them to be 72º. The
distance between the Maverick and the Northern Star is 1527 meters. The Northern Star measures an
angle of 59º between the Maverick and the Throw-Rug. What is the distance between the Northern Star
and the Throw-Rug? (To the nearest meter)
6. AREA OF A TRIANGULAR LOT: A real estate agent wants to find the area of a triangular lot. A
surveyor takes measurements and finds that two sides are 52.1 meters and 21.3 meters, and the angle
between them is 42.2º. What is the area of the triangular lot?
7. Find the side a of ABC given the area, angle C , and side b.
a) Area  163.2 km², C  142.7, b  24.6 km
b) Area  731.9 feet², C  72.2, b  43.8 feet
8. A triangular lot has sides of 215m, 185m, and 125m. Find the measures of the angles at its corners.
9. Solve ABC , given C  28.3, b  5.71, a  4.21
10.
From point C both ends A and B of a proposed railroad tunnel are visible. If AC = 165 meters,
BC = 115 meters, and C = 74º, find AB, the length of the tunnel.
11.
Two sides and a diagonal of a parallelogram measure 7, 9, and 15, respectively. Find the
measures of the angles of the parallelogram.
12.
COST OF A TRIANGULAR LOT: The dimensions of a triangular lot are 100 feet by 50 feet by
75 feet. If the price of such land is $3 per square foot, how much does the lot cost?
13.
NAVIGATION: An airplane flies 165 miles from point A in the direction 130º and then
travels in the direction 245ºfor 80 miles. Approximately how far is the airplane from A?
14.
NAVIGATION: An airplane flies from Ft. Myers to Sarasota, a
distance of 150 miles and then turns through an angle of 50º
and flies to Orlando, a distance of 100 miles (see the figure).
(a) How far is it from Ft. Myers to Orlando? (b) Through what
angle should the pilot turn at Orlando to return to Ft. Myers?
MA42: TRIGONOMETRY
LESSON NOTES
MA42-S9C5-#01,02,03,04,05
LAW OF SINES & COSINES – EXAM REVIEW #01


TSWD analysis of triangles by examining a triangle, identifying its “type”, and then solving the triangle using the
Law of Sines or Law of Cosines.
TSWD analysis of “Real World” Trig problems by examining a problem, identifying & classifying the important
information, and then solving the problem using the Law of Sines or Law of Cosines.
1. Solve ABC , given C  38, b  45, c  42.
2. ANGLES OF A TRIANGULAR PLOT: A triangular plot of land has sides of lengths 420 feet,
350 feet, and 180 feet. Approximate the smallest angle between the sides.
3. METHODS FOR FINDING THE AREA OF A TRIANGLE: You have two methods for finding
the area of a triangle. (a) List the two formula’s (name the formula(s) when appropriate).
(b) Describe when it is appropriate to use each formula (write complete sentences).
4. FIND THE AREA OF TRIANGLE(S):
(a) Find the area of a triangle with sides 10 cm
and 3 cm, with an included angle of 120º.
(b) A businessman wishes to buy a triangular lot
whose sides measure 125 feet, 280 feet, &
315 feet. Find the area of the lot.