Download Trigonometry

Pre-Calculus
Name:________________________
Date: __________
Block:______
Triangles Review Packet
Find the positive and negative coterminal angle, THEN convert the GIVEN angle measure to their
equivalent degree or radian measures. (Give the EXACT COTERMINAL angle)
6
1) 7
2) 76°
3)
7
Find (if possible) the COMPLEMENT and SUPPLEMENT of the following angles.
5
4)
5) 2
11
Find the rounded values of each trigonometric function using your calculator. Round to the nearest
thousandth.
6) csc 23o
7) cot 3
Find the value of  in degrees by using a calculator. Round to the nearest thousandth.
8) sin  = 0.5456
9) tan  = 1.423
10) cos  = 0.124
Sketch a right triangle corresponding to the trigonometric function of the acute angle  . Use the
Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of  :
7
11) sin  =
25
Evaluate the following trigonometric functions without using a calculator: (Find the exact answers)
12) cos 30o
13) sin

6
14) csc 45o
Find the exact value of  in degrees and radians without using a calculator.
2
3
15) sin  =
16) csc  = 2
17) cot  =
2
3
18) From the top of a 74-foot light house on the coast, a person sees a boat of fishermen. The angle of
depression of the boat is 7.6o. How far is the boat from the lighthouse? Draw a right triangle to represent the
problem.
19) Suppose you are standing 300 feet from a 48 foot high tree. What is the angle of elevation from where you
are standing to the top of the tree with respect to the ground? Draw a right triangle to represent the problem.
20) Let Ɵ be an acute angle such that cosƟ = 0.31. Using the Fundamental Trigonometric Identities, evaluate
the following.
a) sinƟ
b) tanƟ
c) cscƟ
21) Two airplanes leave an airport, and the angle between their flight paths is 40º. An hour later, one plane has
traveled 300 miles while the other has traveled 200 miles. How far apart are the planes at this time? Draw a
triangle to represent the problem. Round your answer to the nearest hundredth.
22) You are looking at buying a triangular plot of land. The fencing that outlines the plot of land measures 130
yards, 325 yards, and 245 yards on each side. Draw and label a picture to represent this problem. Find the area
of the land in square yards. Then find the number of acres if 1 acre = 4840 square yards. Round your answer to
the nearest hundredth.
23) John wants to measure the height of a tree. He walks exactly 20ft from the base of the tree and looks up.
The angle from the ground to the top of the tree is 53º. This particular tree grows at an angle of 87º with respect
to the ground rather than vertically (90º). How tall is the tree? Draw a triangle to represent the problem. Round
your answer to the nearest hundredth.
24) Ship A is 32 miles from a lighthouse on the shore. Its bearing from the light house is N 15° E. Ship B is 41
miles from the same lighthouse. Its bearing is N 52° E. Find the number of miles between the two ships.
25) Use the most appropriate formula to find the area of each triangle. Show your work and write a
sentence stating your reason for choosing each formula.
(a)
(b)
(c)
26) A circle has a radius of 20 centimeters. Find the length of the arc intercepted by a central angle of 45°
27) A water sprinkler sprays water on a lawn over a distance of 18 feet and rotates through an angle of 120°.
Fine the area of the lawn watered by the sprinkler.
28) Use trigonometric identities to transform ONE SIDE of the equation into the other.
csc90    cot  sin   1
Solve each of the following triangles. For each triangle, identify the case and which law you would use
first. Round your answers to the nearest hundredth and remember to put units with your answers.
29) A = 113°; a = 12ft; c = 5 ft
30) a = 14 in; b = 23 in; c = 17 in
31) C = 108°; a = 10 cm; b = 6.5 cm
32) B = 65°; A = 67°; c = 14 mm
33) c = 10 m; a = 15 m; C = 45°
34) B = 53°; b = 23 in; c = 27 in
ANSWERS
1) 401°; 7-2π; 7-4π
2)
19
 ; -284°; 436°
45
5) C: NONE; S: π-2 or 1.14
6) 2.56
11)
12)
8
20

3) 154.29°;   ;
7
7
13)
17) 60°;

3
1
2
23) 24.85ft
24) 24.69 miles
26) 5π ≈ 15.71cm
27) 339.29ft2
14)
18) 554.6 ft
20a) 0.95 20b) 3.06

6
; S:
22
11
8) θ ≈ 33.07° 9) θ ≈ 54.90° 10) θ ≈ 82.88°
7) -7.02
3
2
4) C:
19) 9.09°
20c) 1.05
25a) 29.70ft2
15) 45°;
2
30) B ≈ 95.30°
C ≈ 47.39°
A ≈ 37.31°
31) c ≈ 13.51 cm
A ≈ 44.75°
B ≈ 27.25°
33) No Triangle Exists
34) C ≈ 69.64°
A ≈ 57.36°
a ≈ 24.25 in
C ≈ 110.36°
A ≈ 16.64°
a ≈ 8.25 in
16) 30°;
21) 195.13miles
22) 14217.07 yds2; 2.94acres
25b) 19.81 mi2
29) C ≈ 22.55°
B ≈ 44.45°
b ≈ 9.13 ft

4
25c) 65 cm2
32) C = 48°
a ≈ 17.34 mm
b ≈ 17.07 mm

6