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Problem 1
Fill in the blank(s) to correctly complete each sentence.
A triangle that is not a right triangle is a(n) _________ triangle.
Problem 7.33
To find the distance AB across a river, a surveyor laid off a distance BC = 354 m on one side of the river. It is found that B = 112° 10' and C = 15° 20'. Find AB. See the figure.
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Problem 10
Consider each case and determine whether there is sufficient information to solve the triangle using the law of sines.
Three sides are known.
Problem 12
Find the length of each side labeled a. Do not use a calculator.
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Problem 14
Solve each triangle ABC.
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Problem 16
Solve each triangle ABC.
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Problem 17
Solve each triangle ABC.
A = 68.41°, B = 54.23°, a = 12.75 ft
Problem 20
Solve each triangle ABC.
B = 38° 40', a = 19.7 cm, C = 91° 40'
Problem 23
Solve each triangle ABC.
A = 39.70°, C = 30.35°, b = 39.74 m
Problem 25
Solve each triangle ABC.
B = 42.88°, C = 102.40°, b = 3974 ft
Problem 28
Solve each triangle ABC.
C = 79° 18', c = 39.81 mm, A = 32° 57'
Problem 34
To determine the distance RS across a deep canyon, Rhonda lays off a distance TR = 582 yd. She then finds that T = 32° 50' and R = 102° 20'. Find RS. See the figure.
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Problem 35
A ship is sailing due north. At a certain point the bearing of a lighthouse 12.5 km away is N 38.8° E. Later on, the captain notices that the bearing of the lighthouse has become S 44.2° E. How far did the ship travel between the two observations of the lighthouse?
Problem 36
Radio direction finders are placed at points A and B, which are 3.46 mi apart on an east-west line, with A west of B. From A the bearing of a certain radio transmitter is 47.7°, and from B the bearing is 302.5°. Find the distance of the transmitter from A.
Problem 37
The bearing of a lighthouse from a ship was found to be N 37° E. After the ship sailed 2.5 mi due south, the new bearing was N 25° E. Find the distance between the ship and the lighthouse at each location.
Problem 38
Standing on one bank of a river flowing north, Mark notices a tree on the opposite bank at a bearing of 115.45°. Lisa is on the same bank as Mark, but 428.3 m away. She notices that the bearing of the tree is 45.47°. The two banks are parallel. What is the distance across the river?
Problem 39
A balloonist is directly above a straight road 1.5 mi long that joins two villages. She finds that the town closer to her is at an angle of depression of 35°, and the farther town is at an angle of depression of 31°. How high above the ground is the balloon?
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Problem 48
Find the area of each triangle using the formula 𝓐 = ½ bh, and then verify that the formula 𝓐 = ½ ab sin C gives the same result.
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Problem 51
Find the area of each triangle ABC.
A = 42.5°, b = 13.6 m, c = 10.1 m
Problem 53
Find the area of each triangle ABC.
B = 124.5°, a = 30.4 cm, c = 28.4 cm
Problem 55
Find the area of each triangle ABC.
A = 56.80°, b = 32.67 in., c = 52.89 in.
Problem 58
Find the area of each triangle ABC.
A = 59.80°, b = 15.00 cm, C = 53.10°
Problem 59
A painter is going to apply paint to a triangular metal plate on a new building. Two sides measure 16.1 m and 15.2 m, and the angle between the sides is 125°. What is the area of the surface to be painted?
Problem 60
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 m and 21.3 m, and the angle between them is 42.2°. What is the area of the triangular lot?
Problem 1
Which one of the following sets of data does not determine a unique triangle?
a. A = 50°, b = 21, a = 19
b. A = 45°, b = 10, a = 12
c. A = 130°, b = 4, a = 7
d. A = 30°, b = 8, a = 4
Problem 3a
In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
a. two triangles
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Problem 3b
In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
b. exactly one triangle
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Problem 3c
In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
c. no triangle
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Problem 5
Determine the number of triangles ABC possible with the given parts.
a = 50, b = 26, A = 95°
Problem 7
Determine the number of triangles ABC possible with the given parts.
a = 31, b = 26, B = 48°